chore: Trigger Docker release on publish

[keithwillcode]

What does this PR do?

Our new release process wasn't trigger this anymore since we draft and then publish releases.

Mandatory Tasks (DO NOT REMOVE)

• I have self-reviewed the code (A decent size PR without self-review might be rejected).
• N/A - I have updated the developer docs in /docs if this PR makes changes that would require a documentation change. If N/A, write N/A here and check the checkbox.
• I confirm automated tests are in place that prove my fix is effective or that my feature works.

How should this be tested?

• Use our new release process and ensure this workflow is triggered

[graphite-app]

Graphite Automations

"Add foundation team as reviewer" took an action on this PR • (02/05/25)

1 reviewer was added to this PR based on Keith Williams's automation.

"Add ready-for-e2e label" took an action on this PR • (02/05/25)

1 label was added to this PR based on Keith Williams's automation.

[vercel]

The latest updates on your projects. Learn more about Vercel for Git ↗︎

Name	Status	Preview	Comments	Updated (UTC)
cal-com-ui-playground	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 5, 2025 9:41pm

2 Skipped Deployments

Name	Status	Preview	Comments	Updated (UTC)
cal	⬜️ Ignored (Inspect)			Feb 5, 2025 9:41pm
calcom-web-canary	⬜️ Ignored (Inspect)			Feb 5, 2025 9:41pm

[github-actions]

E2E results are ready!

• Workflow #46512.1 latest results