Add TypeScript checking and fix TS issues in wp-tooltip.js

[westonruter]

✅ Committed in r62794 (07a2d76)

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This is a follow-up to r62741.

Trac ticket: https://core.trac.wordpress.org/ticket/51006

Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Opus 4.8
Used for: Debugging and reviewing.

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This Pull Request is for code review only. Please keep all other discussion in the Trac ticket. Do not merge this Pull Request. See GitHub Pull Requests for Code Review in the Core Handbook for more details.

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Props westonruter.

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[github-actions]

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[joedolson]

This looks good to me.