Fix bug with the dt update-version tool

[kenzieschmoll]

Fixes #6623 so that release version updates work as expected when bumping from a non-dev release.

Pre-launch Checklist

General checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I read the Tree Hygiene wiki page, which explains my responsibilities.
• I read the Flutter Style Guide recently, and have followed its advice.
• I signed the CLA.
• I updated/added relevant documentation (doc comments with ///).

Issues checklist

• I listed at least one issue that this PR fixes in the description above.
• I listed at least one issue which has the contributions-welcome or good-first-issue label.
• I did not list at least one issue with the contributions-welcome or good-first-issue label. I understand this means my PR might take longer to be reviewed.

Tests checklist

• I added new tests to check the change I am making...
• OR there is a reason for not adding tests, which I explained in the PR description.

AI-tooling checklist

• I did not use any AI tooling in creating this PR.
• OR I did use AI tooling, and...
  • I read the AI contributions guidelines and agree to follow them.
  • I reviewed all AI-generated code before opening this PR.
  • I understand and am able to discuss the code in this PR.
  • I have verifed the accuracy of any AI-generated text included in the PR description.
  • I commit to verifying the accuracy of any AI-generated code or text that I upload in response to review comments.

Feature-change checklist

• This PR does not change the DevTools UI or behavior and...
  • I added the release-notes-not-required label or left a comment requesting the label be added.
• OR this PR does change the DevTools UI or behavior and...
  • I added an entry to packages/devtools_app/release_notes/NEXT_RELEASE_NOTES.md.
  • I included before/after screenshots and/or a GIF demo of the new UI to my PR description.
  • I ran the DevTools app locally to manually verify my changes.

If you need help, consider asking for help on Discord.

[gemini-code-assist]

Code Review

This pull request updates the vm_service dependency to version 15.1.0 and refactors the version update logic by introducing a centralized calculateNewVersion function, which is now supported by a new suite of unit tests. A critical logical bug was identified in the refactoring: the 'release' type now performs a minor version bump when the current version is stable, but the logic for resetting release notes was not updated to account for this change, which could lead to incorrect release note management.

[auto-submit]

autosubmit label was removed for flutter/devtools/9793, because - The status or check suite Verify PR Release Note Requirements has failed. Please fix the issues identified (or deflake) before re-applying this label.