As far as browsers go, judging from earlier experience with Windows and more recent experience with Linux... After the OS goes unsupported the browser will still work fine, and will get browser updates (on Linux you have to have the browser installed by deb file or as an extracted archive folder, not via the repositories as these would stop updating when the OS stops getting updates), but eventually (possibly several years) the browser will either have an update which makes it no longer workable on the old OS or the browser will complain that it's next update won;t be possible to apply because the OS is too old to support incoming new browser versions.
The other problem here ofcourse is website bloat, each webpage used far less RAM and other resources to load it than they do now. Infinite scroll pages are particularly bad in this regard. I've still got some fairly old computers, with a modern linux OS on them, but when opening many tabs of excessively fancy webpages the age of the machine becomes noticable.
Linux as host, and either Windows in a VM, or if you're really lucky running your necessary Windows programs under Wine (some programs will, other's won't, a matter of luck), is definitely the way to go, and has been ever since the pushing of Win10 via GWX.exe started.