Decent tuner with a headphone output and volume control

Almost every FM station I know of is online these days, if you have a streamer, you are all set.

I have a streamer with volume knob and headphone jack. I seriously know of no reason to "Tune In."
If you do, I think you're stuck with an avr or a crappy used 80's receiver.
A 128 stream on a laptop will sound better than most of those tuning sections. Not to mention screwing with an antenna.

I do the same thing as you in my bedroom system. I used to have a Bryston BHA-1 headphone amp with a SACD player and the Sony XDR-F1HD. I just recenlty sold the BHA-1. I get a great station on the FM dial, which sometimes plays vinyl too. The same station on the internet sounds like crap. I actually bought the Sony HD player solely to listen to the second HD broadcast from this station.

I bought a modified Sony tuner from this guy. I think I paid around $400.
https://www.xdrguy.com/xdr-f1hds-for-sale.html

HD radio is crap but the player also gets regular FM and the tuning is amazing. I also have a Magnum Dynalab MD 102 that cost close to $3K. The Sony is not as good but it is rather close to the same quality. For $400 it is a steal.

This unit does not have a headphone amp but what I will do, to replace the BHA-1, is get either the Headamp GS-X mini for $1799 or a second Benchmark HPA4 for $3K. So at the low end for around $2100 you could have a killer FM headphone system.

Not what you asked but likely better sound quality than what you are thinking.

Listening to my Meze Empy + MD 102 + Benchmark HPA4 as I write this. Awesome sound.

A good FM tuner (and antenna) can provide excellent sound quality, often much better than a streaming version of the same broadcast. I'm not aware of any good tuners with a good headphone amp however. You could look on the fmtunerinfo site or its discussion list. Or get a headphone amp or a preamp with a decent headphone amp to go along with your tuner.

I have two Accuphase T-101's that I use for background music. They have headphone jacks and volume control, but no amp. Stellar sound quality.