I will reply to my own question and ask a couple more
Reptile 500 quad with Pixracer + PX4 stable.
I was able to reduce oscillations on stick input in Pos Hold mode to some degree by changing Position Control PID gains.
MPC_XY_VEL_P has a huge effect. At default 0.09, oscillations on stick input are concerning. At 0.12 they are huge and scary. At 0.06 they are small, but still present.
Increasing MPC_XY_VEL_D from default 0.01 to 0.02 results in different fast oscillations that are always present (not just on stick input). Position control signal is probably not very friendly for derivative calculation. i.e. D-term cannot do a miracle here.
Changing MPC_XY_VEL_I from default 0.02 to 0.03 or 0.01 did not visibly affect the oscillations. I-term is probably slower than oscillations.
Changing MPC_XY_P from 0.95 to 0.5 did not have a visible effect on oscillations.Not sure what this parameter does.
What do I loose by reducing MPC_XY_VEL_P to the min value of 0.06 ? Reaction time to a new waypoint and new stick position in Pos Hold? Does it effectively change max speed (tilt angle)? i.e. I might have a problem fliying in strong wind in Pos Hold mode if position PI are too low?
I am guessing that oscillations are caused by the large stick deadband in Position Hold mode. Maybe something can be done to reduce the effect in the future? Maybe something like subtracting the deadband value from RC input signal in Pos Hold mode to prevent jumping from 0 to 10% ? Obviously, I don't know much about position controller yet and this is just a guess.
I will get to reading position controller code eventually and it will probably provide answers for most of my questions