Remove or replace unused `js-*` classes with `data-testid`s

We should replace the no longer needed js-* classes in VSA both on the group level and project level. We will also need to update some related rspec tests.

The following discussion from !65329 (merged) should be addressed:

• @nmezzopera started a discussion:

  question (non-blocking): Do we need this js- class inside a vue component? We normally use those only for vue app initialisations

• !65329 (comment 618170853)

The following discussion from !66835 (merged) should be addressed:

• @peterhegman started a discussion: (+1 comment)

  nitpick (non-blocking): Can js-path-navigation be removed? Doesn't look like it is doing anything from what I can tell