Upgrade to TypeScript 9.2.0

[henrymercer]

Now that we've dropped Node 12 support, we can upgrade to the latest version of TypeScript!

• I've brought a bunch of other packages up to date, since we need to update our linter and test suite to be compatible with the new TypeScript version.
• I've added type annotations to account for the stricter type checking that's now enabled.
• I've bumped our compilation target from ES2019 to ES2021 (see https://github.com/microsoft/TypeScript/wiki/Node-Target-Mapping).

Merge / deployment checklist

• Confirm this change is backwards compatible with existing workflows.
• Confirm the readme has been updated if necessary.
• Confirm the changelog has been updated if necessary.

[henrymercer]

@github/codeql-action-reviewers This is ready for review. The two checks that are still yellow have been removed, and we'll need to update the required checks prior to merging.

[aeisenberg]

Nice!

This was really hard to review since the PR tools in the browser just wasn't loading the code for me. Or I had to wait 10-15 seconds for rendering.

[aeisenberg]

A few minor comments for typing, but I think it's basically good.

[aeisenberg]

LGTM.