[ci] Default deploy e2e tests to the repo next version (#96895)
This is mostly just to remove some confusion and clean up unused default
values in some places.
When you run on a backport branch or older tag, you probably never want
to use `canary` and just the version at that point. Running on `canary`
branch will implicitly use the latest `@canary` from NPM.
Since our setup job already checks for the version declared in the
checkout, we should use that everywhere so that we only have to check a
single place to be sure about what version is/will be used.
I'll backport this especially because it'll fix a bug in 15.x where we
ignore the release tag.
