[WIP] Migrate project from JavaScript to TypeScript

[Copilot]

• Set up TypeScript toolchain (tsconfig.json, install dependencies)
• Convert root files (index.js, handler.js, full-sync.js) to TypeScript
• Convert lib/ source files to TypeScript
• Convert lib/plugins/ source files to TypeScript
• Convert test files to TypeScript (or update jest config to support TS tests)
• Update package.json scripts for TypeScript build/run
• Create ADR in docs/ folder documenting the migration decision
• Update README with TypeScript-related information
• Validate build and tests pass

Original prompt

Use /js-to-typescript skill to migrate the project from javascript to typescript, create an ADR in docs folder, update the README. This is a github app written in typescript using Probot library.

Created from VS Code.

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