Do "Earlier Operating System" Macs have limitations re access or connection quality to the Internet?

Is there anything about the current Internet / WWW that would affect access to (or connection quality re) webpages when using Earlier Mac Operating Systems (i.e., Catalina) and/or browser versions that are out-of-date (but still perform well) and can't be updated because of hardware limitations?

Wouldn't any such limitations be evident from one or more of the hardware diagnostics that the Apple Store runs when one brings devices to the Genius Bar?

The issue: I'm trying to track down major Internet connection issues that began about 3 weeks ago. ISP thinks the problem is age of computer and/or inability to update to modern browser versions. But I had not experienced any problems until the beginning of the month. Apple Store found no issues with my MacBook Pro and the Internet ran without the problems I have at home while at the Apple Store.

Thanks.