SAS modes and trimming controls

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I don’t know if it’s just me having this issue, but it seems that the SAS damping mode doesn’t work correctly.
In “manual” mode, trim adjustment works.
In “damping” mode, trimming doesn’t work, except for a few aircraft. Even if I trim the controls in “manual” mode, once I switch to “damping” mode, the trim resets to default values.
In “automatic leveling” mode, some aircraft behave as if autopilot is enabled, maintaining course and altitude. However, some aircraft behave exactly the same as in “damping” mode.

Shouldn’t trimming be available in “damping” mode? And shouldn’t “automatic leveling” work like an autopilot that maintains both course and altitude?

automatic leveling does not maintain alt at all and you’ll eventually fly to the ground as the nose dips in attitude.