The Class Structure is mostly intended for New Lights (In Lore) with most guardians being able to mix the structures. That being said, most guardians will also generally stay within 1 subclass as their primary power, only branching out lightly. So, we have the New Lights. They don’t split or drift away from their respective Subclass. We then have the Average Guardian. They don’t drift too much from their primary subclass. You might see one pull of a Blink on Arc, or some other crap. We then have the upper classes of Guardians. They will actively use different abilities from the other classes employed to best suit them. Like when Felwinter used a Shoulder Charge. They will also make use of multiple subclasses (See Ikora) Then we have The Guardian. In part because The Guardian is the player character, they are one of if not the only Guardian to completely bypass the entire subclass and class system in the first place, able to be a Titan, Hunter, and Warlock all at the same time. Mind you, the Guardian is incredibly powerful, more so than the Drifter (Darkage Lightbearer. Not a Guardian, nor does he follow the class system) so this, plus the fact that we bypass the Class system is a testament to our absolute absurdity. On a tangent, I would like to point out that all the D1 subclasses still exist. Sunsinger and Arcblade both being the ones to no longer exist. They only exist within the lore though. And with Final Shape, it seems as though Sunsingers and Arcblades along with their respective counterparts, Dawnblades and Arcstriders, have slowly been combining into 1 single subclass. With the Advent of both Song of Flame (A Radiance like Super) and Storms Edge (an Arcblade themed super) as proof.

The answer is that every individual player plays the canonical guardian. You can see it as everyone plays the events of the game on their own timeline that only differs in a single way (who "The Guardian" is) For every players game every other player is simply another guardian but the player is "The" guardian. So if youre an Exo Warlock then The Guardian is an Exo Warlock, if youre an Awoken Hunter then The Guardian is an Awoken Hunter. Events the player has not done are not done by The Guardian but by other Guardians of that timeline, once the player has done them then you can technically argue you shift timelines to one where your Guardian is The Guardian who did those first.

Canonically, you are playing "the" Guardian's story, but is purposely never stated the race or class of the Guardian. Several stories do this, so that it is written with the player as the hero, everyone else being just another Guardian in your fireteam or in the Tower. So technically it is a weird mix of all three races and classes, kind of like multiple versions of a myth, which means your own head-canon is correct and as valid as the next person's. (Personally, my own head-canon is my Guardian is just re-living the campaign or other activity through a simulation of their recorded events.)