It isn't the macOS that is limiting your access to web pages... it's the Safari browser.
Internet security features continue to evolve and older versions of Safari cannot negotiate secure connections with newer sites, that may or may not actually be adhering to best internet security standards.
If you are having trouble connecting to and using websites with your older version of Safari, try it with a newer third party browser that is still being updated to meet current internet security protocols.
I suggest you take a look at Firefox browser or Brave browser... or even Chrome 🙄.
The Safari browser is typically updated with a macOS update or upgrade. Of course, that only happens if your Mac can support the newer macOS version.