ci: Update workflows to use actions that don't need organization secrets

[jdbaldry]

What this PR does / why we need it:

Each repository can only have 100 organization secrets and there are now more than 100 in our organization which causes inconsistent behavior.

Some repositories don't have the secrets they need assigned.

These composite actions use secrets stored in Vault that are available to all repositories.

• publish-technical-documentation-next.yml has been tested with https://github.com/grafana/writers-toolkit/blob/main/.github/workflows/publish-technical-documentation.yml.
• publish-technical-documentation-release.yml has been tested with https://github.com/grafana/backend-enterprise/blob/gem-release-2.13/.github/workflows/publish-technical-documentation-release.yml.

Which issue(s) this PR fixes:
Fixes https://github.com/grafana/technical-documentation/issues/979

Special notes for your reviewer:

There is some copy-paste involved in the creation of these workflows. Please check:

For publish-technical-documentation-next.yml:

• The on.push branches and paths filters are correct for your repository.
• The jobs.sync.if repository matches your repository.
• The jobs.sync.steps[1].with.website_directory matches the directory you publish to in the website repository.

For publish-technical-documentation-release.yml:

• The on.push branches, tags, and paths filters are correct for your repository.
• The jobs.sync.if repository matches your repository.
• The jobs.sync.steps[1].with.release_tag_regexp regular expression matches your tags and captures major, minor, and patch versions from those tags.
• The jobs.sync.steps[1].with.release_branch_regexp regular expression matches your release branch names and captures major and minor versions from those branch names.
• The jobs.sync.steps[1].with.release_branch_with_patch_regexp regular expression matches your release branch names if they were to include a patch version, and that it would capture major, minor, and patch versions from those branch names.
• The jobs.sync.steps[1].with.website_directory matches the directory you publish to in the website repository.

We'll also need to backport this to any branches where you are maintaining documentation that you want synced to the website.

[JStickler]

[docs team]

[JStickler]

@jdbaldry Will we need to backport these changes?

[jdbaldry]

Yeah, ideally to any branch that you are currently maintaining

[grafanabot]

Hello @JStickler!
Backport pull requests need to be either:

• Pull requests which address bugs,
• Urgent fixes which need product approval, in order to get merged,
• Docs changes.

Please, if the current pull request addresses a bug fix, label it with the type/bug label.
If it already has the product approval, please add the product-approved label. For docs changes, please add the type/docs label.
If the pull request modifies CI behaviour, please add the type/ci label.
If none of the above applies, please consider removing the backport label and target the next major/minor release.
Thanks!

[grafanabot]

Hello @JStickler!
Backport pull requests need to be either:

• Pull requests which address bugs,
• Urgent fixes which need product approval, in order to get merged,
• Docs changes.

Please, if the current pull request addresses a bug fix, label it with the type/bug label.
If it already has the product approval, please add the product-approved label. For docs changes, please add the type/docs label.
If the pull request modifies CI behaviour, please add the type/ci label.
If none of the above applies, please consider removing the backport label and target the next major/minor release.
Thanks!

[grafanabot]

Hello @JStickler!
Backport pull requests need to be either:

• Pull requests which address bugs,
• Urgent fixes which need product approval, in order to get merged,
• Docs changes.

Please, if the current pull request addresses a bug fix, label it with the type/bug label.
If it already has the product approval, please add the product-approved label. For docs changes, please add the type/docs label.
If the pull request modifies CI behaviour, please add the type/ci label.
If none of the above applies, please consider removing the backport label and target the next major/minor release.
Thanks!

[grafanabot]

This PR must be merged before a backport PR will be created.

[jdbaldry]

Will need a repo maintainer to merge this, I don't have permissions