No license plates.

Registration gone.

Swapped tires (obviously a set of identical size)

Took a bunch of trim parts.

Sounds like somebody is fixing up an identical model, totaled car. Stealing
your plates and registration may allow them to (momentarily) pass under the
radar and sell their patched up rig to some unsuspecting Rube.

Normally, you get a damaged car never declared a "total" from a junk yard for
this purpose- but then again it is cheaper to steal one, isn't it?

Very important: Is the dash torn up in conjunction with "trim pieces missing"?
Is the VIN plate missing from in front of the steering wheel? If it is, have
the state watch for a forged "Affadavit of Lost Title" (or whatever they call
the form in your locale).