Configure prettier to run on its own (i.e. not as an ESLint rule)

[soerenbf]

The recommended way to run prettier is to run it on its own and not as a plugin of something else (source https://prettier.io/docs/en/integrating-with-linters.html). I think we should integrate prettier --check as part of our CI instead of running it on lint.

Also prettier by default formats a lot of things aside from js/ts files. Some editors are configured to format files on save, and currently this repository doesn't support that very well, as prettier will run on every file supported by it (unless ignored). This will result in some diffs which consist largely of formatting changes due to being implemented in an editor with this workflow integrated. I would suggest we handle this by:

• [ ] Updating prettier to version 3 (ignores files from .gitignore and .prettierignore by default)
• [ ] Remove eslint integration with prettier, add eslint-config-prettier instead, which simply disables rules which would conflict with prettier)
• [ ] Add .prettierignore to select which files we want to format
• [ ] Run prettier --check along with lint in CI
• [ ] Add pre-commit hook to run prettier on staged files of selected file types (to keep functionality as is)