chore: migrate to ts 5.2.2

[mainframev]

Release notes:

• 5.1: https://www.typescriptlang.org/docs/handbook/release-notes/typescript-5-1.html
• 5.2: https://www.typescriptlang.org/docs/handbook/release-notes/typescript-5-2.html

What's addressed:

• Explicit type roots. Type roots are no longer making upward walking.
• Module and ModuleResolution since 5.2 should match recent node settigns

Previous Behavior

New Behavior

Related Issue(s)

• Implements #32402