chore: update `typescript` to `5.2.2`

[erikian]

• [x] I have read the contribution documentation for this project.
• [x] I agree to follow the code of conduct that this project follows, as appropriate.
• [x] The changes are appropriately documented (if applicable).
• [x] The changes have sufficient test coverage (if applicable).
• [x] The testsuite passes successfully on my local machine (if applicable).

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