While your Mac can't be upgraded to a newer version of the Mac OS, the alerts you are receiving are almost never about which version of the Mac OS you are using, and are almost always about which browser you are using.
The web browser that I've been recommending to anyone who will listen is Brave. Brave is currently the most secure web browser out there (I've tested a bunch of them), it's FAST, it blocks ads natively, it has even better compatibility with odd web sites than Safari, it's just a better browser. And the good news is that it's FREE, and it supports Mac OS 10.11!
Brave browser (free)
The Brave browser is a fast, private and secure web browser for PC, Mac and mobile. Download now to enjoy a faster ad-free browsing experience that saves data and battery life by blocking tracking software.
brave.com
Switching to Brave should solve your problem.
If you are wondering if you need a VPN, I'd say that you don't. It's a matter of debate, but it may be that VPN's are an anachronism that have been made superfluous by current technology:
https://www.nytimes.com/2021/10/06/technology/personaltech/are-vpns-worth-it.html
"The reality is that web security has improved so much in the last few years that VPN services, which charge monthly subscription fees that cost as much as Netflix, offer superfluous protection for most people concerned about privacy, some security researchers said.
"Many of the most popular VPN services are now also less trustworthy than in the past because they have been bought by larger companies with shady track records."