The way I envision this working is with something like git filters. Checking out from version control converts it all into text in your preferred formatting, which you then work with as expected. Staging it converts it into the stored representation. In git, this would be done with smudge and clean filters, like how git LFS works. You'd also have viewers for forges and the like that are built to interpret all the stored representations as needed.

You still work with text, the text just isn't the canonical stored representation. You get diffs to resolve only when structure is changed.

You get most of the same benefit with a pre-commit linter hook, though.