To directly answer your questions: It keeps the old version and a .tmp file (seems to always be listed as 1144KB, but I don't know if that's version specific). This has been happening consistently with all games for quite a long time, on windows 10 (but I'm pretty sure I remember having it happen on windows 7 as well)
I've been having this issue for as long as I've been using the mod (earliest version I can find in my history is from sept 2022.) It'll bring up the update popup, say update completed, I click the apply update button, it says reloading scripts, and 80-90% of the time it comes up with the exact same update popup I saw in the first place.
In the past I'd just kept clicking the button until it eventually worked, but while trying to get a look at the game directory while testing today it got weird. I _think_ the issue I was running into is related to clicking the "apply update" button too quickly, as almost every time that I tried to get a screenshot while updating it would just work. When I managed to break it it was by clicking the apply update button _immediately_ (it shows up without delay) and I'd get the attached image. When I actually waited a bit after it appeared before clicking it I'd occasionally get a glimpse of a .update file, and it'd go through fine.
So at this point I'm pretty sure that the issue I ran into is that I'd click the "apply update" button before the update actually finished downloading, and it'd fail and keep the old version. This was likely exacerbated because once I got used to this happening my default way of dealing with it was to just click the update button, apply the update, and tab out while waiting for it to reload (repeat until it takes) which lead to just mindlessly going fast.