Can I upgrade my MacOS Catalina 10.15.7 to MacOS Big Sur 11?

A late 2013 iMac cannot be upgraded beyond Catalina.

Be aware that Catalina was a quite unusual upgrade that also required updates of any non-Apple 32-bit apps and that Apple gave notice of that in several ways, including in previous updates. It should not have affected anything related to your iPhone. If you are having issues with the phone and Catalina you may want to post about that in a new post to see if anyone can help.

The reference I gave about using Turbo Tax online was not about free tax prep. It was about the Turbo Tax online product that can be used with older as well as current macOS versions and will run with Catalina. But they do charge for it generally, although there are some free options as well in some cases.

Also, since you cannot upgrade beyond Catalina you may want to consider, for security reasons, using a 3rd party internet browser instead of Safari which cannot be upgraded to a current versions. Chrome, for example, supports running their current browser version (with current security features) with Catalina.

What model (MacBook Air, iMac, etc) and what model year is your Mac? Both are available at Apple menu > About This Mac.

Personally, if your Mac can be upgraded I would upgrade to the latest version possible. If you reply with the above information I or someone here can tell you what it can be upgraded to.

If it can't be upgraded, or even if it can, if you are asking about Turbo Tax, a very good option is Turbo Tax online. It can be used on very old macOS versions.