One, due to lack of OS consumer support (ie security patches) from Micrososft, using Win7 or Win8.x for general consumer compute, including Internet, is strongly not advised (unless MS extended support contracts at very high prices and with very limited/select availability for certain enterprise or government clients)
That said, slightly older versions of OBS should work fine on Win7 as an OS
However, I have an ancient ARM based Win8.x system that was a free upgrade to Win10... and Win10 sooo much better than Win8.1 (once you get passed personal annoyance at some MS design decisions... and I get the irony as I'm avoiding Win11 for now in part due to stupid design decisions (start menu/taskbar) and not needing/benefitting from any new WIn11 features.. for now. anyway
Realize that real-time video encoding is computationally demanding. So a low-end system (regardless of OS) may struggle. Many (Most?) Win8 systems worked fine with Win10, so if PC powerful to use OBS to begin with, then I'd strongly consider looking into a free OS upgrade (presuming legit OS license), doing a full diskup backup before, just in case, of course..