Does px4-fmu-v5x_default support GPS_HIL or GPS_INPUT messages?

My pixhawk 5x holybro autopilot.

I am trying to send GPS using GPS_HIL. I have read hundreds of topics about this, but either did not find a solution in them, or the solutions described in them do not work.

I set MAV_USEHILGPS to 1. And expected the result as discribed: ‘Use HIL GPS message even if not in HIL mode’. I received results returned for requests - “Success”. But nothing happened.

With “HITL enabled”, the GPS is received normally, so my mavlink_passthrough.send_message(message) is correct.

I read about this topic in Ardu-Forum. And ArduPilot has the parameter GPS_1_CONFIG = 14, so that the autopilot would receive GPS via Mavlink.
In PX4 GPS_1_CONFIG Parameter Reference | PX4 User Guide
does not have this option, but something like: 401: Pixhawk Payload Bus.
QGroundControl does not know about such a parameter, but I entered it manually.

I went through dozens of variations of EKF2_AID_MASK, remembering how long it took me to get the Vision position estimate to work properly, until I found that QGC has a bug and just checking the boxes is not enough and you need to enter the value manually.
Need I say it didn’t work?

I spent so much time on this…

And I come to the conclusion that the PX4 either does not support this function, or … I’m desperate …

Please advise the correct steps…