See:
For info about the changes that need to be made to the stac-fastapi Filter Extension conformance class constants to align with the conformance classes defined in CQL2 final.
Once these are in, the stac-fastapi-pgstac implementation will need to use them. I haven't looked at what it's currently advertising. Looking at the pgstac code, I think it supports almost all of the conformance classes, except maybe IN (#215)?
The one odd thing that it may not support is that the Basic Spatial Functions class was changed to require only support for s_intersects with a Point or a bbox ({ "bbox": [0,0,1,1]}), and it may not have support for the bbox literal.