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I've pulled, pushed, twisted, wiggled and nothing is budging. I'm not even sure where to bulb ends and the adapter begins. Guessing the metal ring is part of the bulb? Spent hours on youtube and forums and found nothing helpful. The only examples are later models, which have different assemblies. Any help is much appreciated.

That looks like a bodge to me.
The bulb should be held in place via a clip and the igniter which screws onto the back of the headlight housing.
Does the other side look the same?
How did you remove the igniter?

Edit:
looking a bit closer at your photo, you probably can't remove that connector as whoever has bodged it together probably soldered the wires to the bulb connectors. It may even have been supplied like that from an aftermarket supplier.

It's def not standard but doesn't look so dangerous, at least the bulb end looks like it's isolated well with a double sheath and at the other end they enter the terminal block of what I suspect is the igniter unit which is probably aftermarket and look isolated.
I hope you disconnected the battery before fiddling around? There's some considerable voltages knocking around xenon headlights!

Yeah, not standard at all. Doesn't look like mine at all.

Does the bulb still work or are you replacing them?

Do you know if the car has been upgraded to xenon?

Yes, looking into replacing the bulb. It often turns on for a few minutes before going out. Hope it's not a bigger issue. Was going to try swapping the bulbs to see if that fixes this lamp, but ran into the above problem.

Hadn't even considered I might be aftermarket. That would explain not finding any info on this setup. I've only had the car a couple years with next to no info from the previous owners. Pretty sure there was front end damage that was fixed, so wouldn't surprise me that the lamps are aftermarket.

I'm assuming the igniter is the metal box holding in the bulb that I've seen in diagrams and videos. This doesn't seem to exist in my assembly. There was just a thin metal clip that held the bulb in place.

So maybe there is a clip further up the wires. I'll go check it out.

Update: These are in fact aftermarket Hella lamps, a slightly different part number from these. Pulling the bulb assembly out further, it looks like the wires clip in. Now I've hit another wall. I don't see any xenon bulbs on the market that come with wiring like this. Also I haven't been able to find any installation or bulb replacement videos that might shed light on what I'm dealing with.

As stated before, the bulb itself does not budge and there is no noticeable seam where I would expect it to detach. Either it's really jammed, there's some trick to detaching the bulb that I can't figure out, or it's built into the wiring as a pre-assembled product I can't seem to find.

Your thoughts would be much appreciated

they look perfectly stock to me for an aftermarket kit. Most seem to have long leads and connectors on the bulbs. example being here https://www.amazon.co.uk/Xenon-Conversi ... NrPXRydWU= this is just a random kit I found on Amazon. HTH

Oh nice, that looks right! I just didn't know what to search for.