No Safari update is available in the App Store

I keep getting messages that I need to update my browser - Safari Version 13.1.2 (13609.3.5.1.5)(2003-2020). There is no update available in the App Store. As I have researched, It's suggested that I upgrade my MacOS, High Sierra 10.13.6, there is no upgrade path. I then receive a message that there are incompatible updates available. So what do I do? Get a 3rd party browser such as Chrome? Get a new computer? ( I can't afford one at this time).

Turn-off my wifi and stop using using this computer on the internet?

[Re-Titled by Moderator]