Test against multiple TypeScript versions in CI

[JoshuaKGoldberg]

(starting from scratch because there isn't a repo build steps focused issue template)

Splitting out an issue for #2516 (comment):

We don't yet have any test tooling around specifying TS versions (for any package).
On the to-do list but nobody has ever prioritised it.

The simplest approach might be extending CI's unit_tests_on_other_node_versions to also switch on different TypeScript package versions (example syntax).

It'd be great as a next step (followup issue?) to also make use of CodeCov's report merging to combine unit test coverage from all of them. #2516 is an example PR where code under test changes behavior on the TypeScript version.

[bradzacher]

We should probably centralise discussion about this on #1752

[JoshuaKGoldberg]

Aha! I searched but didn't find that one. Thanks!