Egregoros

These are clearly inspired by Mirror's Edge

Glass Horizon looks less interesting to me, it's too much of a straight rip-off and it doesn't even look as good as the original. What are we doing here?

The second is Vholume and that tries to do its own thing. Looks a bit like SPRAWL, if you played that (if you haven't: don't) or brutalism in general. This is very much the modern canon interpretation of Mirror's Edge's aesthetics. Video essayists claim it is a "love letter to concrete" and this game tried to capture a RAW concrete look, "beton brut".Mechanically clearly very close too. Sounds phenomenal, too. I will play this.

It may seem odd that none of these have taken off, considering the popularity of gender reassignment psyops (speedrunning)

When I scrubbed through the Steam pages for all these I noticed a pattern.
And no, I don't want to talk about ambient DnD again. Although I really like it.

When I think back to defrag or surf, I think a central aspect is that it was so community driven, with all other players appearing as ghosts, new local records being announced in chat, and voting for the next map. Of course, the maps themselves were community made as well.
So Celaria leaning into that isn't that much of a surprise to those who played others in the scene.

Aesthetically, defrag and surf maps have vastly outcompeted all of these new contenders, for the simple fact that Surf can lean on the Source 2 engine, and even defrag had global illumination via lightmaps. That grainy re-encode I put in the op may not do it justice, but it was VERY smooth to look at, and that became its own aesthetic in Quake circles. People loved those low frequency textures and color bands. That may have influenced or been influenced by the release of Mirror's Edge too, but idk.
It can be very hit or miss to go for that look deliberately, because without advanced lighting techniques for the mappers, it becomes very boring very quickly.

Mechanically, I guess it's laudable that Hoverflow and BOOST VECTOR EX try to do their own thing, although I would be worried about it sticking.

Anyway, what is a good name for these types of games?

>Honorable mention: That Teeworlds grappling hook mode.

@DrRyanSkelton I never felt that 3D sonic actually lent itself to fun, "smooth" high-speed gameplay, so this might be more correct than you intended.
It's an interesting space in game design, and so far many have tried, but none have succeeded, in catching this particular type of lightning in a bottle. So who knows if successful "movement mechanics" can even be introduced deliberately.
Perhaps looking at Titanfall would answer my question. People say that flows nicely, so I would be interested in how much of that was intentional.

What would a success look like in this genre?

After all this, the music choice is obvious.
Sound-design should be very minimal and I would even be very careful about rushing air sfx. Many people play these with their own music on, and you're never gonna replicate people's 200 hour Spotify playlists. So perhaps integration would be a viable alternative?

Basically every single one that we've seen has a massive graphical disadvantage compared to the quake and cs mods, that goes without saying. CS has advanced shader materials, but if you were to do this properly, you should probably go for a lightmapper.
This is a tremendous technical undertaking for the following reason

Since these all kind of failed already at making high-speed mechanics happen deliberately, perhaps a straight up clone of either quake or CS movement would be for the best. I've seen successful additions to it in the various quake forks, such as wall jumping and a grappling hook. I can't speak to surfing.
And when you go for a clone, you clearly need the ability to import maps from the predecessor. You have to either support Source Engine or id tech 3 .pak maps. Combining this with a modern lightmapper isn't easy, but I believe it would pay off if the game could on-the-fly recompile the lightmaps for improved lighting in your engine and buffer those to disk.

Since you are not taking off like some coal mainstream shooter, the community must stay your main focus. Quick Play should probably be just an auto search through the community servers, and you could even consider making those "fake", by which I mean you just host them yourself and give the admins control over the map rotation and server settings. You'd need an algo to demote the unpopular ones.
You would definitely want like 5 to 10 people per lobby, and I would absolutely preserve the voting aspect.