To echo a lot of people here, I'm less than a fan of the new UI layout or search window; I'd much rather the old UI was kept as much as possible on top of your new backend improvements. If the old wouldn't work with your new systems/framework for whatever reason, at least keep the general style of it.
The best way I can describe my experience with the new UI is to say that it feels like someone has smeared vaseline over the main mod page, objects on it aren't all clearly defined or distinct from each other, sections are almost unnecessarily large overall, and I miss the colours that were present before, as they immediately drew the eye to important/relevant information. The "Popular Collections" section might be nice for other people, but it's entirely irrelevant to me, so a function to disable it (or other elements) would be really nice to have. Not required at all though, as people like me who don't like it will find other ways to hide it.
The mod browsing page is a mixed bag, with the filters being the least objectionable. Making the filters a hideable sidebar instead of a dropdown seems like neither an up- nor downgrade, again I prefer the old dropdown, but the new is completely fine imo. I don't know how popular this is, but I prefer the tiles for the mods to be smaller, and while vertical empty space irks me quite a bit, I have less problem if it's horizontal; thus, if the tiles were just a smidgen smaller or there was one less tile per row, the browsing wouldn't really be any different from old, apart from already-stated colouring issues. The missing time range feature would be really nice to have back.
The mod pages themselves haven't really changed much yet, from what I can tell, apart from becoming darker and breaking the visuals of some mods (can't remember which honestly), but that could be because of the author and, as such, out of your hands. There are, however, some weird things happening with the background colours of the mod pages:
I honestly can't remember if that was there before the update, if it was, please disregard this point. Just please don't put the mod page through a similar update, it really doesn't need it, the colouring changes are enough.
I'll say nothing more about the search feature than that it needs improvement, which I understand you're already working on. Oh, one more thing: please make the "Mods" tab the default, or at least a preference to change it.
I understand you (Nexusmods) have poured a lot of time and resources into this update and are not going to change the course you're on right now, but I do think you're moving the wrong direction with this UI change; the old was distinct, this new one feels just like every other website redesign in recent years: modern, sleek and soulless. Yes, there is a lot of people outright dismissing this update, I was one of them during the beta (I took one look at the beta and opted out, so I guess I'm part of the problem), but also a lot of helpful, constructive criticism here. You need but listen.
The way I see it, people like me who don't like this update have two options:
Begrudgingly accept that this is how the site will look from this point on while grumbling unhappily about it until we don't notice the problems any more (honestly, the thing I'm expecting for you to bank on), or
Go to another mod hosting site, however they tend to be smaller, more specialised on a few games, have less/worse features, or all of the above.
Or the secret, third ending: leave and make their own mod hosting site, with blackjack, and hookers! Not probable in most cases, and even less likely to be profitable in the long run.
Yes, right now there are a lot of outbursts, but not always unfounded, from the loud minority who found this update not to their tastes. The rest will either like it, suffer in silence or leave. This update won't be the end of Nexusmods, just as the "Modpocalypse" wasn't, but it will drastically downgrade the experience of users like me. I highly doubt you'll see any notable downturn in usage because of the update, but I still wish you'd take the design back a few steps toward what you had before.
Thank you for still maintaining this site, it's invaluable when modding most games, despite some of your decisions through the years. I'll still use the site, and as they say, "this, too, shall pass", and I do believe that.
TL;DR: Rambling. The new UI is a mess to me and many others, people can be arses about things that do not matter in the grand scheme of things, I do not expect anything to meaningfully change for the better from here on.