Implement #5748

[Rich-Harris]

Edited: this now incorporates #5782 and #5810.

This PR implements #5748.

• [ ] use the app's installed TypeScript rather than including it in SvelteKit (i.e. don't generate types otherwise)
• [ ] make write_types work incrementally
• [ ] update the docs
• [ ] get all the tests passing
• [ ] ensure all the migration guides are correct
• [ ] other stuff, probably

[changeset-bot[bot]]

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Latest commit: 99690ae935ec19a59b4d4ea5dbedd07e55b06a41

The changes in this PR will be included in the next version bump.

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