That standard format is commonly known as source code - although it lacks a normal form.
Tools like prettier, gofmt and black can be thought of as a way to produce a normal form of source code.
This is (IMO) a reasonable incremental approach towards exactly what you describe - if a project checks in only source code that's formatted using a standardised format, then you're free to work on it using whatever equivalent representation you like - as long as it's converted back at commit-time.
The challenge for a tool like difftastic is that I can't guarantee that syntax is well-formed. You might be using new syntax that my parser doesn't support, you might have merge conflicts, or you might have a plain syntax error in your code.
Tree-sitter handles parse errors gracefully, so difftastic handles syntax errors pretty well in my experience.