gh-pages workflow should be tested

[thehowl]

@Villaquiranm see this workflow fail: https://github.com/gnolang/gno/actions/runs/12888293723/job/35932866096

I think we should do two things:

1. Ensure we test the build workflow even in PRs, so if this workflow breaks we know ahead of time. (Possibly also for the other gh-pages workflow, maybe we can use the same workflow file but avoid publishing to the branch).
2. We should not use GOROOT as the variable where to store the GOROOT variable, as it overrides the GOROOT determined by the go binary and can cause a mess; so I'd say we replace that with something like GOROOT_SAVE.

We should also specify in the README of stdlib_diff that the version being checked against is the toolchain version in the go.mod.

[Villaquiranm]

Sure @thehowl I've created a PR for it thanks 💯

#3607