Don't push tags in our custom release script

[Andarist]

In https://github.com/changesets/action/actions/runs/30812557230/job/91682567379, I noticed this:

/home/runner/work/action/action/node_modules/.bin/changeset git-tag
🦋 changeset v3.0.0-next.8
25l◇  Created tags:
   - v2.0.0-next.4
25h[command]/usr/bin/git push origin refs/tags/v2.0.0-next.4
remote: Bypassed rule violations for refs/tags/v2.0.0-next.4:        
remote: 
remote: - Cannot create ref due to creations being restricted.        
remote: 
To https://github.com/changesets/action
 * [new tag]         v2.0.0-next.4 -> v2.0.0-next.4
Warning: Failed to create tag v2.0.0-next.4: Reference already exists - https://docs.github.com/rest/git/refs#create-a-reference

In this draft PR, I'm just exploring various tag-related improvements. I don't want to land this PR now - gotta rethink all the implications.

[changeset-bot]

⚠️ No Changeset found

Latest commit: f818768

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