Fix Typescript errors and clean up TS configs

[fredrikekelund]

Related issues

Fixes STU-1373

Proposed Changes

We currently have a few TS errors in our code. This PR addresses that with the following changes:

• Add a typecheck npm script.
• Update AGENTS.md to tell agents to do type checking.
• Run that script as part of the lint CI job.
• Removed "*": [ "node_modules/*" ] resolvers in tsconfig.json files. This means it's no longer possible to import any code from node_modules files. Instead, we use regular module resolution to import available modules.
  • This may sound like a big change, but it's really not. I only had to apply a minor edit to a single file (use-update-button-tooltip.ts) to make this work.
• Install @types/glob and wpcom to prevent TS from complaining.
• Add a patch to fix the lookup path in yargs for the locales directory, fixing the same issue as Fix Studio CLI yargs locale strings displaying in English #2609.
• Fix all other type errors

Testing Instructions

CI should pass.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[fredrikekelund]

The __dirname relative path lookup fails because we bundle yargs into apps/cli/dist/cli/main.js. Weirdly, translations still worked for me even without this change (after I reverted https://github.com/Automattic/studio/pull/2609)… In any case, this change produces the correct path.

[wpmobilebot]

📊 Performance Test Results

Comparing 623c5b4 vs trunk

site-editor

Metric	trunk	623c5b4	Diff	Change
load	1759.00 ms	1730.00 ms	-29.00 ms	⚪ 0.0%

site-startup

Metric	trunk	623c5b4	Diff	Change
siteCreation	6056.00 ms	6087.00 ms	+31.00 ms	⚪ 0.0%
siteStartup	3953.00 ms	3942.00 ms	-11.00 ms	⚪ 0.0%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)