Hmm, yeah this might be tricky to get to work well. My current head units sadly were non Bluetooth models from 10 to 15 years ago, so I use a Esinkin Bluetooth receiver plugged into my car stereos AUX input, which is essentially what the old cassette adapters add to your tape player, added an AUX input to them. It has a decent frequency response and sounds good. I have another cheap brand BT adapter which sounds horrendous / distorts fast, so BT adapters are not all the same quality.
Note: the esinkin adapter has RCA outputs, and a 1/8” output to feed into a stereos AUX input. Use one or the other. Point being, you could plug a standard cassette adapter headphone plug into it via the 1/8” output. It runs on 5v so I use a cigarette lighter USB charger with it.
Also, some of the cheap cassette adapters are garbage too, last one I bought did not work anywhere near as good as an older Sony one from the 90's I also had that I needed to fix the cord on (I think it was a Sony brand), so swapped the cord to the Sony and junked the cheap one. So some of the cassette adapters do not work well if at all, I'd stick to older name brand ones.
Link to the BT adapter I use that works well.
So something like this:
Plugged into this:
Being powered by one of these:
I've been running it like this into my AUX inputs on my headunits and it sounds totally normal. Use my phone to set the input level, then the car stereos volume control from that point on. Not sure if it will work with a cassette adapter as well, but perhaps something to try if you don't care for the BT FM adapters. This setup sounds much better than the FM adapters I used.
At any rate, good luck with it.