There are a couple of stolen bike registries on the internet.
They may not be tied to the police databases. But, I assume it is due diligence to try to look up a bike in the registry.

If the vicitm posts a serial number, then it should be pretty easy to get a match,although at least Trek has a pretty confusing serial number on some of their bikes.

Looking for bike features is more complex, and depends somewhat on how rare the frame is and whether it is being resold locally.

My old Viscount was stolen years ago. My parents filed a police report and insurance claim.
About 2 years later, the police reported to a burglary, and stopped a man riding a bike near the crime.
One of the officers apparently commented "That is a bike thief" and they demanded to see the serial number.
The rider showed them the S/N, and it was found to be stolen.
The police confiscated the bike, and charged him with theft.
In court, it was determined that the police did not have probable cause for the search, and the rider was let go (without the bike).
Most of the parts on the bike had been swapped for cheaper parts.
I had already replaced the bike so we allowed the insurance company to reclaim it. And I don't know what happened after that.
I have no idea if the person on the bike was the "thief". It is quite possible that he had bought a bare frame (and may have known the thief), and built up the bike with spare parts he had. He, of course, lost his wheels, tires, derailleurs, and etc that had been mounted on the frame.