Yeah, it does. This can sometimes require launching steam in Big Picture Mode first, then select the game you want. A bit annoying to take that extra step but Steam has upped their ps5 controller support lately.
But I play mostly from gog, and my Intel GPU doesn't play nice with the steam overlay (transparency becomes black and everything becomes 5 fps)
Also it means I have to waste 15 precious minutes troubleshooting the game. Pad isn't recognized, try via steam, add it manually, see if it works via xinput, and so on.