In my experience, bluetooth audio latency has made watching videos completely impossible, extremely annoying to be hearing something and not seeing the lips of the person moving the right way.

One of the elements in your system is either very old or borked.

I have an AppleTV4K, and everything is perfectly synced with at least 3 brands of Bluetooth headphones - an 3-year-old eKids one, a 1-year old TaoTronics one, and a 2-year old nameless one.

In the early PlayStation 2 days, many flatscreen TVs (both Plasma and LCD) had delays that made games like Guitar Hero unplayable, so the games added a latency estimation/calibration setting you could use; My 12 year old Onkyo HDMI receiver has a special "eliminate latency in game mode" setting which disables some processing features and reduces sound latency by 50ms or so.

It's not that there were never problems; But anything made in the last 5 years or so, especially using BT4/BT5, should not have these issues.

Edit: just tried with an 8 year old or so JBL Clip I found lying around, and it does have ~100ms latency (estimated, not measured). But the newer ones don’t have it.

IIRC both VLC Player and mpv allow you to set a keyboard shortcut for increasing/decreasing audio-video delay and are capable of streaming directly from YouTube (and I believe any website supported by youtube-dl).

I use mpv and whenever I get audio latency from my headphones* I just adjust in the player.

* - It seems like there's some adaptive algorithm where they start off at 0ms latency but if they experience one hiccup they increase to 250ms-300ms and then another hiccup causes them to jump to 500ms. This is also why a keyboard shortcut that let's you adjust the exact a-v delay value is useful beyond just setting the value once.