I don't know if the new Warlock arc melee or the Titan solar melee experience the same thing, but at least for the Hunter Melee Tempest Strike, quite a few melee perks do not work with it. I don't have a comprehensive list, but it's enough to show how it doesn't work even though it was just another melee ability.
Edit: Updated from new mod system
[u][b]Tempest Strike works with:[/b][/u]
[Deprecated] Melee Wellmaker
Right Hook (if it doesn't kill)
Well Rounded (if it doesn't kill)
Grave Robber
Lightning Weave (Spark of Frequency)
Spark of Feedback
[Deprecated] Striking Light (CWL)
Assassin's Cowl
[New] Heavy Handed
[New] Melee Kickstart
[u][b]Tempest Strike does not work with:[/b][/u]
Right Hook (if it kills)
Well Rounded (if it kills)
The Lethal Current Aspect (in its entirety, including blinding jolted targets)
Impact Induction
Liar's Handshake
Combination Blow (at any amount of stacks)
Disorienting Blow
[Deprecated] Well of Ions (no damage increase [i]AND[/i] it uses up the buff)
Does not break invisibility (Related to Assassin's Cowl, Trapper's Abush, and Rat King)
One-Two Punch
[New] Focusing Strike
[New] Sealed Ahamkara Grasps
[u]Couldn't Tell:[/u]
Pugilist (no perk indicator for handling, and hard to see the difference)
That's all the things I found via Tempest Strike testing. Needless to say, many important things do not work with this. Even though it says in the aspect that we are activating a charged melee ability. I hope these things are fixed soon since it used to work with quite a few of the listed things before Arc 3.0. If this is the same for the other classes' new melee abilities I would like to hear about it.
[Update] Since season 21 is back to focus on arc. I want to push this through again to get these perks and mods working with Tempest Strike. Especially after the mod system rework as this is a serious oversight when trying to build craft as many of the melee-specific mods don't properly work
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+1 this. It used to work with Liars Handshake but since Arc 3.0 the interaction has broken