Okay, I think I've found my ultimate Bluetooth setup. I'm currently wirelessly listening to my mixer through an ordinary pair of audio-technica ATH-M50X headphones*, and the latency is so low that I can't even tell it's there. My microphones are not Bluetooth, but they are very high-quality and low-latency. If I wanted, I could be listening through earpods, or even airpods (with extra latency of course). Every individual part of this setup is replaceable and none of them have built-in cables or inaccessible pairing processes.

My Bluetooth transmitter is the bizarrely-named FlooGoo FMA121 from Flairmesh. It's USB-powered but has a 3.5mm input, and the app lets me select which of those I want to actually hear. The (accessible!) Windows app says my latency is about 15 MS, and I believe it.
The receiver is the Avantree AuraGo AS70P, which is a tiny clip-on device with a 3.5mm headphone jack and a few basic buttons.
The transmitter and receiver both use Bluetooth LE Audio, which is fairly new and supported by almost nothing. That's how I'm able to get such low latency. It's also the thing that powers Auracast, which you may have heard of. But Auracast is a public broadcast that anyone can join (though it does have optional encryption), and what I'm using is Unicast, the single-device version of it.

The FMA121 transmitter also has mobile apps and a Linux version, which I haven't tried. I was pleasantly surprised by the Windows app though. It has minor accessibility issues but nothing that gets in the way of actually using it, especially if you know even basic object navigation or flat review commands. The software is fully open-source and Flairmesh is an Australian company that sells their Bluetooth modules to businesses. They seem to have a refreshing and rare attention to detail.
I haven't yet tried the app for the Avantree receiver because I haven't needed to. It does apparently have an equalizer, so I'll look at its accessibility at some point.

My only complaints so far are (1) it's a bit difficult to switch between different receivers in Unicast mode. The Avantree receivers don't have very good audio feedback and the transmitter seems to have a fiddly pairing process when switching between connected devices. I might reach out to Flairmesh about it. For now, I'm paired to one of my receivers, and I'll just have to keep it charged so I don't have to switch to the spare.
(2) I can't find a short cable that fits my headphones, because despite many 3.5mm cables claiming they work with headphones, they don't often list the measurements for the plug housing, and the jack on my headphones is recessed in a tiny hole.
I've already posted about wireless microphones; we have a few options for those. In particular, the Rode Wireless Pro (not to be confused with the Wireless Micro) has a 3.5mm output on its receiver, and each of the transmitters have a 3.5mm microphone input. This brings us full-circle--I have analog Bluetooth to my headphones, and analogmicrophone audio back to whatever I want. Generally the microphone is going into a computer, but if I wanted to--for instance--send microphone audio to my computer through a Zoom recorder and also send the audio to my phone through its USB connection, I could do that. For most people who don't need to do that, the Godox C01 or Rode Wireless Micro are much cheaper and better options.

I've tried out a lot of wireless headphones and Bluetooth transmitter/receiver pairs over the years; this is not the only option out there, but I would say it's the best modular option I've been able to find.

I should probably just write a blog post about all this, but that would require me to have a blog.

* The audio-technica headphones are the Bluetooth version, the ATH-M50X BT2. But I have never used the Bluetooth mode. At the time I bought them, they were almost the same price as the regular ones, and I like that they use a generic 3.5mm cable instead of Avantree's proprietary 2.5mm twist-off cable.