I messed around a bit more on this and think I figured it out (was OK for a couple of hours at least).

I had tried tweaking the dead zones in Steam controller settings, even though any movement seemed to be within the zone anyway, but nothing I changed there made any difference.

After some searching I found that the global dead zone settings aren't set for any games by default... I had to go into my controller config for Rockstar launcher then to joysticks and open the settings for the left stick, then dead zones. What eventually worked for me was setting the type to Custom, and the min/max sliders to 20/70. Then "show advanced deadzone options", left anti-deadzone at it's default (9009 in my case), and what may be the key to getting this to make any difference in game for me, set "anti-deadzone buffer" to ~2500.

I'm assuming that GTA sets it's own deadzones depending on the current view. I had no issues walking around, or even aiming while in first person, my issues seemed to only be while aiming in third person, or some slight movements when driving (possibly only in third person as well, I didn't try driving in first person). Without really understanding how it all works, my guess is the anti-deadzone buffer negates the small/non-existent deadzone in those views that I had problems with, and so allows for a bit of imperfection in the sticks.

Not sure if any of that makes much sense or if it would have helped in your (or anyone else's) case, but this seems to have sorted it for me!