Upgrade TypeScript to 6 in backend, e2e, and validation

[yoga-teachedison]

Context

TypeScript has been upgraded to ^6.0.3 in the frontend, but the rest of user-office-core is not aligned:

• apps/backend still declares typescript: ^5.3.3
• apps/e2e still declares typescript: ^5.3.3
• validation does not declare TypeScript directly and currently receives it through the ts-jest peer dependency

This leaves packages using different compiler versions and makes the validation build depend on peer dependency auto-installation.

Scope

• Upgrade backend and e2e to TypeScript ^6.0.3
• Add TypeScript ^6.0.3 as a direct dev dependency of validation
• Upgrade supporting TypeScript tooling where required for TypeScript 6 compatibility, including @typescript-eslint, typescript-eslint, ts-jest, and ts-loader
• Resolve TypeScript 6 compiler or configuration errors in these packages
• Regenerate the affected lockfiles

Acceptance criteria

• apps/backend/package.json declares TypeScript ^6.0.3
• apps/e2e/package.json declares TypeScript ^6.0.3
• validation/package.json declares TypeScript ^6.0.3 directly in devDependencies
• The affected package lockfiles resolve TypeScript 6 without incompatible peer dependency warnings
• Backend type-check, build, and unit tests pass
• E2E type-check and lint pass
• Validation build and tests pass
• Existing e2e tests pass, or any failures unrelated to this upgrade are documented

Related

• Migrate deprecated tsconfig options before TypeScript 7 (target, moduleResolution, baseUrl) #1706 tracks frontend tsconfig options that must be migrated before TypeScript 7.