navbar_alerts: Convert module to TypeScript.

[afeefuddin]

Self-review checklist

• Self-reviewed the changes for clarity and maintainability
  (variable names, code reuse, readability, etc.).

Communicate decisions, questions, and potential concerns.

• Explains differences from previous plans (e.g., issue description).
• Highlights technical choices and bugs encountered.
• Calls out remaining decisions and concerns.
• Automated tests verify logic where appropriate.

Individual commits are ready for review (see commit discipline).

• Each commit is a coherent idea.
• Commit message(s) explain reasoning and motivation for changes.

Completed manual review and testing of the following:

• Visual appearance of the changes.
• Responsiveness and internationalization.
• Strings and tooltips.
• End-to-end functionality of buttons, interactions and flows.
• Corner cases, error conditions, and easily imagined bugs.

[afeefuddin]

The cancelled check seems unrelated.

[zulipbot]

Heads up @afeefuddin, we just merged some commits that conflict with the changes you made in this pull request! You can review this repository's recent commits to see where the conflicts occur. Please rebase your feature branch against the upstream/main branch and resolve your pull request's merge conflicts accordingly.

[timabbott]

The cancelled check seems unrelated.

Yeah, that usually just means GitHub Action's infrastructure didn't run it, often because a new version was pushed.

[timabbott]

Merged, thanks @afeefuddin!