In my interactions across several different cities my impression is that PSL is full of comrades but it has some bad organizational habits. Those habits lead to distrust of them by other groups with which they should otherwise be natural allies. The criticisms you listed are well-known. I'll validate some of them, though keep in mind I'm not advocating against PSL, I just think the org has taken the wrong approach to these issues and is making itself look bad in attempts to save face (or other reasons).

PSL has a habit of rallying the wagons rather than properly handling issues. That's the common thread between La Riva flipping out over being called cis (lol), poorly handling sexual assault allegations, and the "we don't like what you've been posting on Twitter" stories, all of which are real. I'm not even being creative here, PSL folks said that they have to be vigilant against CIA and NGO types and tied this to their actions like... sharing the real name of the person alleging sexual assault. For the record, the accuser was being threatening towards others and should've been expelled before the PSL unforced errors.

They're also notoriously kinda mediocre at running protests. This is a very qualified criticism because they're also often the only group cool enough to organize them and create coalitions (ex via their front groups) so I'd say this is just something to keep in mind if you're organizing with them - they probably need help when it comes to planning the logistics, training people, keeping it safe, etc because that seems to be either not a priority or outside their capacity. Or maybe I'm just spoiled by working with groups that are 100% on top of that. This might be a reason to join PSL if you have experience doing these things as you'll be able to make the org tangibly better.

Finally, they're also well-known for being terrible at recruiting and onboarding, which is the main reason I've never personally joined. Not because I personally had trouble, I'm just tired of being in orgs that care more about a national statement or whatever than core groundwork (my local PSL people are currently obsessed with their presidential campaign). You'll express interest in joining and never hear back. Or you'll hear back four weeks later and play phone tag until someone forgets about you. This seems to vary regionally but it's still a deal breaker for me and I'm not surprised that other local orgs are growing faster.

To me, the open question is whether those bad habits can be overcome internally or whether another very similar org will displace them eventually when those bad habits create a split.

If you're not in any org right now, though, joining PSL is not a bad idea.

Finally, I think thru really, really need to come up with some kind of strategy to deal with the bad (for lack of a better word) PR because in a ton of orgs/coalitions I've worked with, people raise the issues you posted, OP, and it often leads to PSL being excluded from the coalition. In response, it's not easy to stick your neck out with "here's why doxxing someone making sexual assault accusations was bad but not so bad we shouldn't work with them", lol.