fix(codegen): write prettier-stable generated manifests

[kitlangton]

What

Formats the `.httpapi-codegen.json` manifest through prettier (json parser, repo print width) at write time, instead of raw `JSON.stringify(..., null, 2)`.

Why

The last red job on v2 CI. The generate bot (running on v2 since #41207) executes `script/generate.ts`, which ends with a repo-wide prettier pass — collapsing the short manifest arrays to single-line before committing. `check:generated` in `packages/client` regenerates without that pass, producing multi-line manifests, and `git diff --exit-code` fails:

```
-["client-error.ts", "client.ts", "index.ts"]
+[

• "client-error.ts",
  ...
  ```

Generated `.ts` files were already prettier-formatted at write time; the manifest was the one artifact that wasn't. Making it prettier-stable at the source fixes the check regardless of whether the bot's format pass runs afterward.

Testing

• `packages/httpapi-codegen`: typecheck green, 87/87 tests (manifest expectation updated to the prettier-stable form).
• `packages/client`: `bun run check:generated` passes against the committed (bot-formatted) manifests — regeneration is now byte-identical.