In case this helps anyone: last night I ran into a similar issue. OBS Studio 29.0.2, macOS 13.3.1, Mac Studio M1 Max. I've been using the "macOS Screen Capture" method set to "Window Capture" for months without problems. Suddenly last night the screen capture froze in the middle of the stream. Worked fine for three hours but suddenly it was happening after recoding for just 5-7 minutes. After a ton of troubleshooting I finally realized I only had 5GB of free space on my main drive.
If you're actually *out* of space you'll get errors from OBS and macOS so it's easier to figure out what's happening. But apparently the new screen capture method will start failing just from being *low* on drive space, without any warnings. (I even dug through the OBS logs and Console and couldn't see anything pointing to the problem there!)