If you're using the lowest latency codec your headphones support, no there's nothing you can do.

That's the limitation of wireless technology at the moment.

I'm not a headset gamer guy so I haven't looked into it that much, but I doubt any conventional bluetooth headphone would be very good latency wise; you'd probably need a latency-optimized protocol (that would likely not be stellar quality-wise). There's AptX LL but it seems pretty poorly supported.

Wonder if anyone makes analog RF transmitter dongles/recievers you can plug wired headphones into? Cursory googling doesn't find much.

Sometimes if you pause your music or video for about 5 seconds, it catches up

That's usually found in the field of pro audio equipment.

Indeed, < 3 ms

https://www.shure.com/en-US/performance-production/louder/shure-whiteboard-digital-wireless-latency-explained#:~:text=Total%20System%20Latency&text=As%20mentioned%20above%2C%20a%20Shure,in%20your%20entire%20audio%20system.

Interested to hear if you get the bathys, please post a review, I'm considering them as well, I gave my xm4s away because they were really good at noise cancellation. And that's about it. Do you get delay while using anc? At the same time as bt? I have no idea if this would cause it?

I have the Sony wh-xm4 and wf-xm4 buds, when I've watched video on my MacBook with them they will connect with AAC, I don't notice any latency on YouTube or with streamed movies. With my phone I use LDAC at highest quality and don't notice latency with YouTube or streamed movies. I mostly use wireless DAC/amps with LDAC and don't get latency with those either. I don't play any games, I imagine that if there was going to be latency it would be with games.

Unfortunately, No.

Unlike wired connections, in wireless world - audio data needs to be cut into small segments called 'packet' to efficiently communicate with multiple devices, multiple tracks, and more. It even send the same packet multiple times to counter signal loss! And those packets need to be reassembled into an actual sound signal we can hear.

Every process like these require some time, and it would need some serious technological breakthrough to eliminate the delay while maintaining good audio quality.

Is there any reason why keyboards or mice can have virtually nonexisten input delay with wireless, but audio can't?

1. the input data, which keyboard and mice transmit is much smaller than audio data. this makes difference to encoding delay. due to its size, audio data needs to be encoded following codec's specifications. AAC takes generally 60ms to encode, and LDAC takes 30ms.
2. if your audio device has ANC, it takes even more delay to process audio data. and if your audio device is two separate stereo earbuds, it requires additional delay to sync sound each other.
3. unlike in ear earbuds or headphones, Keyboard and Mices have enough space to put much larger antenna, much larger battery. it enables much stronger signal connections, so manufacturer can greatly shorten packet retransmission delay.

bluetooth keyboards do have latency. generally below 50ms, which is hard to feel for most users. but some competitive gamers still feel latency and prefer wired one.

Fortunately, Bluetooth LE Audio - Completely made from ground up, solves several problems that Bluetooth Classic Audio has. using LC3 - new default codec for LE Audio like SBC - is expected to be able to achieve 80ms - 150ms delay while transmitting 16bit/48kHz audio.

Yes there is! The Bathys support aptX-Adaptive which has a low-latency mode. This mode lowers the audio delay from about ~270ms to only ~62ms. You can visit aptX's website for more info about this mode here: https://www.aptx.com/aptx-adaptive. And here's another link to the focal's latency measurements: https://youtu.be/itzCkCaVcTU?t=251

(for reference, popular wireless gaming headsets have around ~30ms of delay.)

However, you cannot take advantage of this lower latency unless you also have an accompanying supported device (transmitter). I would recommend the Creative BT-W4 Smart Bluetooth Transmitter. It supports aptX-Adaptive (including the lower latency mode). And its reviews make mention of very low latency when gaming using another aptX-Adaptive headphone, the Sennheiser Momentum 4's. It's probably your best bet to achieving low latency on PC.