Unfortunately, something between OBS Studio newer versions, the operating system and Facebook has been causing issues for a while. See other threads in this forum on exact issue
though I didn't go deep enough into issue to figure out if an Operating System certificate issue, the newer OBS Studio versions relying on Win11 OS sub-system, or ??? Facebook itself has clearly been the source of some problems... though I can't say if related to your issue or not.
the fact that you are on Win11 23H2 could definitely be a cause (maybe not, but I'd upgrade to 24H2 and use policy/registry edit (as you prefer) to prevent going to 25H2 for the time being)
Personally, I set up our live stream to use a Scheduled Video so livestream URL is always the same. And for security reasons, we did NOT use a persistent stream key. We used FB's /live/producer to get current service stream key, and act as digital usher. And used an older OBS Studio version... and we didn't have an issue.
We did have the issue of /live/producer not displaying the preview video in Chrome (on Win10) for a while (almost a year ago?), but Chrome and Facebook server HTMP updates resolved that.
