The macOS version you can upgrade to depends on the year your Mac was released.
Click the (Apple) menu at the top of your screen and choose About This Mac.
Check the Compatibility of your Mac with newer versions of macOS:
➡️ macOS 11 Big Sur is compatible with the Macs listed here
➡️ macOS 12 Monterey is compatible with the Macs listed here
➡️ macOS 13 Ventura is compatible with the Macs listed here
If your Mac is incompatible with the newer macOS versions, you may still be able to use TurboTax's online version.
If you cannot make a secure web connection with Safari, then give another browser a try.
Firefox browser and Brave browser are two that I believe will run in Catalina and are still being updated.