Your best bet is probably going to be something like a wired FM transmitter hooked up to a bluetooth adapter with the appropriate charger and cables hooked up to your original head unit. There's probably people out there that will modify them for you to add an input, but I wouldn't know where to look or how much they charge, and in my experience a wired FM transmitter sounds fine.

Hardwired FM transmitters are what usually get recommended. https://www.amazon.com/iSimple-IS31-Antenna-Modulator-Aftermarket/dp/B002U5XPBE/

Have you looked at FM modulator/injectors before? SIMILAR (this may not be the exact one you need) to THIS. They go between the stereo and the antenna and put a perfectly clean FM signal right into the stereo. They come in Aux & bluetooth varieties. A pure FM signal is very high quality, however not as good as CD or what you are describing. It may be easier to implement, though.

This is going to be a lot better than a wireless FM transmitter, if you don't want to replace the stock head unit: https://www.amazon.com/iSimple-IS31-Antenna-Modulator-Aftermarket/dp/B002U5XPBE/ref=asc_df_B002U5XPBE/
It installs between your existing antenna and your factory head unit.

>for that matter FM works

Hardwired FM transmitter. https://www.amazon.com/iSimple-IS31-Antenna-Modulator-Aftermarket/dp/B002U5XPBE/ref=sr_1_2?crid=2Z56IV7V3Z3R1&keywords=isimple+fm&qid=1684392573&s=electronics&sprefix=isimple+%2Celectronics%2C203&sr=1-2

EDIT: You said BT, not just aux in. https://www.amazon.com/iSimple-Hands-Free-Calling-Streaming-Smartphones/dp/B00FRU5UNA/ref=sr_1_2?