(Added a link for anyone who might want to read all of what I wrote. but not have to search through the comments here to find where it's continued.)
Eververse came out back in Destiny 1 during The Taken King, if this article is accurate (https://www.polygon.com/2015/10/12/9512577/destiny-the-taken-king-new-emotes-carlton-dance), it came out specifically on October 13, 2015. At it's creation it only sold emotes and only for silver, at this time you could also only have one unique emote equipped at once.
Then came the first Festival of the Lost in October of the same year and Eververse got new seasonal emotes (you could still buy the original Eververse emotes), emotes you could only buy during that event, but it also got some new items. Specifically a loot box, called Legacy of the Lost, were you could get masks. Yes, you could get masks by just playing the game and collecting candy to fill bags up at that time, but those free masks would become unwearable after the event. Where as the ones you got from the loot box from Eververse would stick around and still be wearable after the event ended. As well as there was one mask, the Skull Mask, that you could only even find by opening those loot boxes, but it was also as an additional drop so you could have got it with another mask. (You did get one of the Eververse, Legacy of the Lost, loot boxes for free when you first talked with Eva Levante during the event)
A few things you should know about those loot boxes though is,
1: there was no knockout list for rewards you could get from them
2: dismantling the masks you got from the loot boxes didn't give you any currency you could use to buy other Eververse items
3: what dismantling did give you though was an item, Paper Glue, which you could use to upgrade the free masks to allow you to keep those masks after the event
4: those mask were purely cosmetic they had no power at all and didn't even have any perks to use during the event
5: in-regards to the Skull mask being a possible additional drop with another mask this is where we see guaranteed loot pools where you got one of the rewards listed under it and possible loot pools where you could get up to two rewards under them, begin to pop-up with Eververse (the mask was the only cosmetic item in this possible lost pools the other possible items where event exclusive/usable consumable items.)
(while not covering all the aspects of what was written here's a source for that that covered a lot of what was https://destiny.fandom.com/wiki/Festival_of_the_Lost)
Next Eververse update happened in December, and we saw a few things happen. First, Eververse's inventory changed you could no longer buy the emotes that Eververse started out with directly; you could still get them but you would have to buy a mystery bag that gave you a random old emote; and instead new emotes were being sold. Along with that though, was that when you got your weekly nightfall reward you had the chance to get a mystery bag that would give you one of the previous Eververse emotes that you didn't already have. Again, this was just a chance and you weren't guaranteed a mystery bag to drop and you only had as many chances as you had characters for that week. Second, there was a new seasonal event at the same time SRL (Sparrow Racing League) and while it was fun and brought a new limited time activity it also brought with it it's own limited time Eververse items. Besides the one seasonal emote this event had for sale, these Eververse items were again in loot boxes. I say loot boxes because there were two for this event, a Sparrow Toolkit and a Custom Horn Kit, and they brought two new cosmetic type items to Eververse, Sparrows and Sparrow Horns which dropped from those loot boxes respectively (except there was one sparrow, the EV-43 Lightrunner which would only drop from the Custom Horn Kit). Now you could also earn horns through participating in SRL, but at the same time they were like the free masks for Festival of the Lost, where they would not be usable after the event ended. So if you wanted to keep a horn you had to dismantle an Eververse acquired horn to get a Horn Relay, which you could use to make another horn into a permanent version of the horn. Although also during the event you also had a chance at getting a Custom Horn Kit as a nightfall reward. Although there was one more seasonal item brought to the Eververse store, and which was met with controversy even from (and I hate to even talk about him at all even to back a point up) Datto, which was the SRL Record Book, Vol. 1. This item kept track of you stats thought the whole SRL event, times finished first, laps completed, fast lap, etc., it also gave you rewards for achieving goals in those stats, sort of like rewards for certain triumphs. Getting technical, with the rewards you could get from this book you could say Eververse started to sale armor, an emblem, and a shader at this time (it also had a sparrow reward, but sparrows were added to Eververse along with this event as previously stated). Now while the armor had perks that helped during the event there was also free armor you could get as well for the same amount of work and had the same perks so I would still consider the armor from the book purely cosmetic. The controversy over the book was not so much over the rewards, but more of that something to keep track of your stats for you to easily see should have been added. One other thing to add to this part is that the Sparrow Toolkit actually worked on a knockout list, but anything they dismantled didn't turn into anything you could use to purchase other Eververse items.
(possibility of old emotes dropping as nightfall rewards https://gamerant.com/destiny-the-taken-king-emotes-nightfall-rewards/)
(a source mentioning Datto commenting on the SRL Record Book as well as a video that show the contents of Eververse at that time https://planetdestiny.com/bungie-free-events-eververse/)
(list of SRL rewards and how to obtain them https://www.destinypedia.com/Sparrow_Racing_League)
Crimson days was the next time Eververse was updated in February 2016, but that only added 5 seasonal emotes and changed nothing else about Eververse so I won't go into any more detail about it.
(While this shows all of what Eververse sold it also shows it only sold those emotes during Crimison day if you didn't believe me https://www.destinypedia.com/Eververse_Trading_Company)
The next update for Eververse came out in April 2016. A few things were seen with this update, another change of emotes (with a new mystery bag so you could still get the old emotes) and a new type loot box, Sterling Treasure, with two new armor sets (and glows for one of the armor sets as well as Faction vendor armor and some Reef weapons, which were one time use), two new ship and a new sparrow were also possible drops along with an armor piece. All of the armor was in the guaranteed loot pool, but everything else was in the possible loot pool including more instances of the class items of both armor sets for all the classes. Again, this time you still had a chance to earn old mystery bags from doing nightfalls as one of the possible drops. For the first time though you could also earn one of the loot boxes being sold, the Sterling Treasure one, as a guaranteed reward up to three times per account. One for free from the postmaster, one for doing a crucible match, and one for doing the hardest difficulty of Prison of Elders. Allowing you to get some Eververse gear without evening having to spend money on Silver. Although, that did come to an end on September 8, 2016 for at least two of the three free sources, postmaster and crucible. Also again, no knockout list, no currency from dismantle to use to buy other items.
(April update https://www.bungie.net/en/News/Article/44609)
(September update https://www.bungie.net/en/News/Article/45172/7_Destiny-Update-090816)
The next update to Eververse came with Rise of Iron in September 2016. The update saw new emotes and a new loot box, Radiant Treasure, which brought with it a new cosmetic type ornaments (as well as a loot box exclusive emote, Finger Wag, which was in the possible loot pool). You could get one of these loot boxes free each week by doing a SIVA Crisis Strike. From this loot box also came two type of ornaments, exotic weapon ornaments and a token you could use on any iron banner armor to change it's look (this token type of ornament was in the possible loot pool). With those ornaments came something else as well, Silver Dust. Now Silver Dust didn't act like Bright Dust at this point, when it first came out it was used to apply ornaments to weapons and armor, which you need 5 Silver Dust to Apply one ornament. There was only two ways to get Silver Dust as well, either by Radiant Treasure were you would only get one or by dismantling an ornament. Yes, you read that write at first you could dismantle ornaments meaning you would lose the ornament altogether. At the same time, even after using the Silver Dust to apply the ornament to a piece of equipment, if you wanted to revert to the old look, even for a little, it would mean losing the ornament for the weapon and you wouldn't even get the Silver Dust back from that application. Again no knockout list for the loot box, but this time they added something to use for other cosmetics that wasn't event related for dismantling cosmetics.
(explaining how ornaments worked in Destiny 1 https://destiny.fandom.com/wiki/Ornament)
(showing how ornaments used to cost Silver Dust to apply https://www.bungie.net/en/News/Article/45464/7_Destiny-Update---12132016)
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Ppl REALLY this upset over cosmetic items? Good grief!