#40187 fix(apps): resolve strict-mode TypeScript errors in packages/apps/src

Proposed changes (including videos or screenshots)

Fix all TypeScript strict-mode errors introduced when the packages/apps package was configured with strict: true, noImplicitReturns, and noUnusedParameters. Errors included:

• Map.get() used without non-null assertion after has()/set() guards
• Catch clause variables typed as unknown (now cast explicitly)
• Missing return statements in all code paths (TS7030)
• Unused parameters renamed with _ prefix
• Optional chaining / nullish coalescing for possibly-undefined values
• Bridge do* methods returning undefined as unknown as T for denied perms

Issue(s)

Steps to test or reproduce

Further comments

Related to the "Apps-Engine split" stack:

• #40183
• #40184
• #40185
• #40186