Type check errors running tsc --noEmit

[didavid61202]

Environment

Node: v16.13
Nitropack: v0.4.4

Reproduction

open the following Stackblitz clone repo will automatically run tsc --noEmit start command, then errors are logged in the Terminal panel.
https://stackblitz.com/edit/github-tkzhuy?file=.stackblitzrc

Describe the bug

After running type check using typescript's tsc --noEmit commands, shows the following errors:

Errors  Files
     1  examples/cached-handler/routes/index.ts:1
     1  examples/custom-error-handler/routes/index.ts:1
     1  examples/plugins/plugins/test.ts:1
     1  src/presets/aws-lambda.ts:5
     1  src/presets/azure-functions.ts:12
     1  src/presets/azure.ts:10
     1  src/presets/firebase.ts:12
     1  src/presets/node.ts:5
     1  src/presets/stormkit.ts:5
     1  src/runtime/app.ts:43
     2  src/runtime/cache.ts:44
     1  src/runtime/client.ts:5
     1  src/runtime/entries/cloudflare.ts:30
     2  src/runtime/entries/netlify-edge.ts:16
     3  src/runtime/entries/service-worker.ts:33
     1  src/runtime/utils.ts:16
     1  test/fixture/api/kebab.ts:1
     1  test/fixture/api/param/[id].ts:1
     1  test/fixture/api/wildcard/[...param].ts:1
     1  test/fixture/routes/prerender.ts:3
     1  test/tests.ts:74

Errors can be separated into 3 parts:

1. examples/ directory: .nitro folder wasn't built yet for examples in the examples/, which we can ignore for 'source code type checking' as end-users will build those types correctly when they are building those examples.
2. test/ directory: also missing .nitro folder with corresponding types, which we should ignore for test/fixture as it can have its own tsconfig.json for type checks. (can be partially fix with feat: enable response type infer for API routes with params #222)
3. src/ directory: most type errors occurs, some are due to global type's name collision, some are missing discriminating union or mismatch input value.

Additional context

No response

Logs

No response

corresponding PR: #269