Replace non-null assertions with proper null handling in `RealAppsEngineUIHost`

RealAppsEngineUIHost.ts currently relies on multiple TypeScript non-null assertions (!) to bypass strict null checks.

While this satisfies the compiler, it introduces unsafe assumptions that may lead to runtime errors such as:

TypeError: Cannot read properties of undefined

These assertions should be replaced with proper null handling to improve runtime safety and make failure cases explicit.

Problem Areas

The file contains non-null assertions in the following contexts:

• getUserAvatarURL(username)!
• username! inside room members mapping
• slugifiedName!
• getUser()!
• username! inside getClientUserInfo

These assume values are always defined, which may not hold true for:

• Direct Message rooms (may not define name)
• Members without usernames
• Missing logged-in user
• Undefined avatar URLs

Start in RealAppsEngineUIHost.ts and inspect the listed non-null assertions alongside the types and callers that provide those values. Define explicit behavior for missing avatars, usernames, room names, and logged-in users, then validate the changes with the repository's TypeScript checks and existing tests.