Replace TextEdit as the default text editor in MacOS Big Sur
Have you tried SwiftDefaultApps? It's a modern replacement for the old RCDefaults System Preferences pane.
https://github.com/Lord-Kamina/SwiftDefaultApps
Here are two screen shots of SwiftDefaultApps, the first showing Uniform Type Identifiers tab for public.plain.text with Sublime Text 2 set as the Editor, and the second showing the Applications tab and Sublime Text 2 with public.plain.text checked. (This works the same with Sublime Text 3 too.)
With these settings, any plain text file, with or without a .txt extension, will open in Sublime Text when double-clicked in Finder.



 Historical Reference: RCDefaultApp @ web.archive.org: https://web.archive.org/web/20200312011847/http://www.rubicode.com/Software/RCDefaultApp/