As I understand, OBS loads everything on startup, and doesn't care anymore after that. So you can replace, update, delete, whatever, the files while OBS is running, and it doesn't make any difference. (assuming it doesn't lock the files, which is also possible, but it still only looks at them when it starts)
Any settings that you changed are written out on a successful close, overwriting whatever is already there at that time. So if it crashes, it doesn't save your setting changes, which might be good or bad, depending on the situation. (could wipe out a lot of work, but doesn't keep a bad setting either, which may cause it to crash on startup)
Anyway, yes, you do need to restart OBS. And if you've tried a bunch of things, forgotten some of them, and left it weird because of that, you might have some "interesting" troubleshooting to do. Or it might "just work" anyway. Who knows?
24/7 can be tricky for several reasons, one of which is that there's no good time for maintenance. So you have to make that time.
If you really want true 24/7, then you should think seriously about having at least two production rigs (don't have to be equal) and a way to switch from one to the other, live. The switch should be minimal on your end - no production value of its own, just a "nice" switch from the listeners' perspective and nothing else; not a general-purpose PC that runs a bit of software to do that, but literally incapable of anything else - so that it CAN run for years without updating or getting hacked.
It'd be worth looking into whether your streaming platform supports that sort of thing already: two devices streaming to the same thing, with either manual- or priority-switchover in a way that doesn't wreck the mood. Whichever rig is not live at the moment can then have its regular maintenance, including security updates, feature upgrades and related testing, reboot, etc., maybe even move to a different studio if the switch supports that, without interrupting the listeners.
Generally, anything that doesn't have a redundant counterpart, really wasn't that important. How seriously do you take its job?
