You're not the only one!

I found a similar situation when I fixed the driver's window in my 2001 x5 3.0 last week. This was a problem when I bought the car last month, so I really don't know the history.

When I got the panel off, there was no vapor barrier.

The clip on the aft regulator cable was mangled but still attached, giving the window some functionality - it would go almost all the way up if you helped it along. The clip on the forward regulator cable was completely missing, along with the clip/bushing/screw that attach to the window more directly. There was some shrapnel inside the door, but not enough to account for these missing parts. My only guess is that someone tried and failed to hack it and figured they'd sell the car.

There are 2 things that are called "clips" here, and I found it initially confusing: the piece of plastic that directly contacts the glass is called a clip - I'll call it a window clip; also, the metal/plastic part that connects the regulator cable to the window clip is also called a clip - I'll call it a regulator clip. There is no PN since BMW does not sell it separately. They can be found on ebay for about $14/pair.

I ended up replacing everything: vapor barrier (51-48-8-402-389), window clips (51-33-8-254-781), bushings (51-33-8-242-760), screws (07-14-7-154-229), door panel clips (most were cracked) (51-41-8-224-768). When figuring out where to get the regulator clips, I found an aftermarket (Evan Fischer EVA16772019251 from Amazon) complete regulator, including regulator clips for $30, so I bought that, thinking I was getting the regulator for about $18 since I would not need ti buy regulator clips. 51-33-8-254-911 would be the PN for the driver's complete regulator.

It all went in just fine, and I'm glad I bought all the new clips, etc. rather than trying to zip tie it, etc. as you may find.

So to answer your questions more directly:
My question is, do I therefore need an entire regulator assembly, or do I just need a new clip?
If the forward one is fine (I would not count on that), at a minimum you need the window clip, screw, bushing, and regulator clip (off ebay). But not the whole regulator assembly. May as well repair the forward one as well though - it will just double the parts price from $10 up to $20.

I'm thinking the front clip is still intact, since I can lower the window with the passenger door switch after having pulled the window up manually.
Yes, still attached, but my guess is that it will be mangled. The regulator clip is a metal/plastic molded part (i.e., the plastic is molded onto/around the metal so it cannot be repaired with new plastic, just replaced) - on ebay you will find variations on all plastic, to different parts metal vs. different parts plastic. But it's probably mangled.

When I did mine, after disassembly and waiting for the parts to arrive, I semi-permanently propped the window up with a modified broom handle that was screwed into place.