What I mean is that despite having deadzones set in Steam AND in game, I can still walk around the ship by simply placing my thumb on the stick and slightly shifting the pressure, not actually moving the stick, since my sticks have no natural deadzones.
And slightly off topic side note: You should have stopped using DS4W back in 2016 when Steam added support for the Dualshock 4. It has more features, and a huge community that makes and shares profiles for games that don't have native support or improves on the existing support in games. Works for non-Steam games added to Steam as well, as long as you can get the overlay working. DS4W is trash and has been for a long time by comparison. (Even one of DS4W's predecessors, PGP had a community site for sharing profiles. DS4W was subpar from the start)
If you're using an original Dualshock 4 or Dualsense, then you might be experiencing stick drift, which would be a slightly different problem from the game ignoring deadzones UNLESS you have those deadzone sliders maxed and it's still ignoring it. The Dualshock 4 and Dualsense have natural deadzones so you should not normally be able to do the thing I do with the pressure movement. (I have 2 Dualsense in a drawer next to me, both ended up getting stick drift in less than a year each. I also went through 7 DS4's over the course of 4 years. I love the touchpad for Steam input features, but their sticks are ass compared to what I have now.)