It'll be a massive mess, for sure, but I think a lot of people are going for a worst case scenario, or an outright fantastical one (I'd encourage people to look up what the left thought would happen if Trump wins, compared to what actually happened).
Yes, elements of the left will likely go utterly berserk trying to "make sure there's never another Trump" and try to take revenge for being thwarted in 2016. Keyword "elements". Major democrat lawmakers are not even 100% onboard with court packing, and that's an idea that is at the very least legal and on paper (if not in practice) an entirely legitimate use of congressional and governmental power. And multiple senators and representatives have already publicly refuted that plan and refused to go along with it. If they can't even get people onboard with that, it's absurd to believe the government will be able to pull off some mass purge of political dissidents.
"Ah," you say, "but that's only what the government will do, you're ignoring antifa and BLM and so on". Put bluntly, you're clearly buying into those group's own claims of how tough and capable they really are. If they actually had anywhere near the numbers needed to pull of that kind of assault, they'd have done it by now. There is, at best, a tiny lunatic fringe (within the larger, but still tiny lunatic fringe) that actually believes any of their ultra violent rhetoric, most likely a scarce handful. If that wasn't the case, then someone would have actually acted on it. And I don't mean "acted illegally in a heat of the moment confrontation because they're long on aggression and short on brain cells", I mean "gotten a bunch of dudes together and shot up a conservative protest group" or something similar (the same applies regarding left wing fears of the right wing militia groups that they've been freaking out over since the 90s). There's a strong possibility of escalating violence between militant left and right wing groups, and I'll be surprised if there isn't a major firefight between the two groups at some point in the next couple years, but I doubt they'll become something the average right wing american needs to concern themselves with. Ditto for attempts to drive anyone pro-trump out of a job.
That's not to say it's smooth sailing, they'll probably try something (I'd suggest gun control, but a major anti-police bill is more likely their first move), but it's not going to be as bad as you guys are suggesting.
As for specific questions in the OP:
How does this loss shake up right wing politics and mean for the party between now and 2024? and furthermore with Trump probably permanently given his age who will take up the mantle of the face of the party in the near future?
I don't think it means much for right wing politics, actually. Trump has generally be a conventional-ish republican in office, all attempts by the media to hype up every single misstep and problem as "the greatest threat to American democracy since FDR tried to...uh, do a thing that's totally fine and a legitimate use of power", I don't think there's any of his policies the average swing voter would view as being utterly disagreeable, outside of his poor handling of the wuhan flu (which, with a few years of hindsight and distance, will also not be nearly as bad as it's being made out to be right now). If Trump loses, it's because people are not enamored with Trump as a person, his personality, habits, etc, rather than his policy (and also because of our traitorous media class).
As for his replacement....could be any one of a number of people. Cruz, Rubio, or Pence are IMO the likely front runners, but the GOP has a lot of entirely respectable people with national appeal that could easily take over, particularly if the Biden-Harris admin turns out to be as ugly as is feared (as in how it's feared by, like, reasonable people on the right, not by you lot). There's a non-zero but still low it could even be someone like Romney.
