Being free open source, OBS support is as you can get it. So... here is my $0.02 as only an end-user
- With WIn10 being a free upgrade (even today), I don't see any reason normally to stick with Win7 (and I'm avoiding for now Win11, basically still an in-progress Beta). Granted there are certain older Apps that have a problems with WIn10, but most of those have work-arounds. There are some aspects of MS trying to be more Apple-like that annoys me with Win10, but most of those are disabled easily enough. With similar resource demands, the only Win7 I still have around are VMs for historical purposes, and they haven't been booted up in years (having nothing to do with OBS).
- real-time video encoding is computationally demanding, and is therefore inappropriate on really old hardware (the primary reason to stay with Win7). But unless on govt/similar SA agreement and still getting Win7 updates from MS, one shouldn't be connecting to the Internet on a Win7 PC.
So, I question the premise. What real reason is there to stick with Win7 this many years after mainstream patches stopped being publicly available? I do get why in a validated manufacturing environment, with an isolated, restricted VLAN, why Win7 (or older) may still be running on very specific fixed task PCs. bad practice, but I get it). But consumer use? no, bad idea
As for OBS, you could go with an older version on Win7, but why? obviously if something breaks with v27.1.3 on Win7, then that would impact your decision. But I'd start with latest, and just be aware of the multiple methods of display vs game vs window capture, and options within each of those. Some were written for Win10 and may not work on Win7, but others may work fine.
Personally, I haven't needed the features of OBS 27 and I'm stilling running v26 on Win10. You need to look at which features you need, any plug-ins, etc, and review their requirements. Many current plugins have tie-ins with new APIs in OBS v27. So if you need a specific plug-in, that may dictate your OBS version.