Situation as described in the question. We first suspected a partial freeze (temperatures have been extremely and unusually low here in Austin), but even after hours of running the steaming hot trickle, nothing improved. All other pipes seem fine, and opening other faucets doesn't seem to affect the issue – so I don't think it's simply a lack of water pressure in the system.
I'm starting to think it must be some partial mechanical blockage. We do have a hot water tank, and the bathtub is the first branch line after the tank. Could a) the extreme temperatures, b) the main line repair, or c) the fact that we let the bathtub faucet drip all night to prevent the pipes from freezing, somehow have caused this? Could the dripping have dramatically accelerated calcification with chalk sediments from the hot water tank, for example?
Unfortunately, I can't access the 5 or so feet of pipes where the problem must originate from.