Task: T76549: NLA Strip influence slider doesn't respond to autokey correctly.
Source of Problem: (anim_sys.c) nlastrip_evaluate_controls() -> animsys_evaluate_fcurves(): I believe the issue is due to NLA evaluation, where the animated strip properties are evaluated and flushed at the same time the action strip channels are evaluated. Since autokeying doesn't insert a keyframe as the value changes, that's probably why the slider is unresponsive.
Solution: Perhaps we should separate (despgraph-wise) NLA strip animated property evaluation from when we evaluate the NLA system for general animation? Animated strip properties would only be evaluated and flushed on frame change or when the whole frame needs refreshed. Then normal non-NLA animation evaluation will just read the strip properties as is. This would allow the slider be responsive. It also allows the user to change these properties and view their changes without having to keyframe, just like any other Blender animated property.
Potential Problems with Solution: What do we do when strip influence is animated and the user changes it (without keying) then inserts keys on character bones. When we remap the keyframes, should we re-evaluate and use the strip's animated influence? Or should the new keys be remapped using the unkeyed strip time?