Cannot make an Alt Hold stable

It’s mounted on fairy stiff and thick mounting tape. But… I have tested the EKF2 estimator on the same setup and MPC* parameters and it worked perfectly! Rock solid altitude hold. It confuses me a lot: how come the mc_pos_control works differently with different estimator? And I am pretty sure that the LPE is fine: the position follows the LIDAR without any significant delays…
I have also tested the LPE v 1.7.0 and it did not help. Here are some logs:
LPE: https://logs.px4.io/plot_app?log=6f315b12-3887-4432-9aa5-1a47b14f6eee
PX4: https://logs.px4.io/plot_app?log=4e6c8836-fd98-44be-a7df-637eb7fd08fa