Thank you for such an extensive answer. I tried most of these points before writing the post (I know, I should have written it in the question). I wouldn’t like to create the Physic-Base for character control from scratch. I implemented the following solution which works. I just don’t know if this is the right approach or if it will cause me many other problems in the future.
I created a new cube and set its Collision Presets to ignoreOnlyPawn. EventTick then updates the position of this Cube so that it is slightly higher than the Cube affected by PhysicThruster. Thanks to this solution, BP_ThirdPersonCharacter does not collide with the physics object, and at the same time can move around the flying object.
Is this approach ok?