refactor: migrate to TypeScript strict nullish checks

[anxkhn]

Problem Description

The tsconfig.json should enable strict nullish checks for better type safety.

Context

Enabling strictNullChecks catches more bugs at compile time but requires code changes.

Files to Investigate

• tsconfig.json - TypeScript configuration
• All TypeScript files - Fix resulting type errors

Steps to Reproduce

1. Add strictNullChecks: true to tsconfig.json
2. Run pnpm typecheck
3. Observe type errors

Expected Behavior

Code should pass type checking with strict nullish checks enabled.

Acceptance Criteria

• Enable strictNullChecks in tsconfig.json
• Fix all resulting type errors
• No implicit undefined
• Proper null/undefined handling throughout

Suggested Approach

Enable the flag, then systematically fix each type error with proper null checks.

Difficulty: Hard

Estimated time: 3-6 hours
Prerequisites: Advanced TypeScript
Learning outcomes: TypeScript strict mode, null safety