Code quality polish

[sebmck]

Summary

This PR does the following:

• Adds catch handlers to all uncaught and unhandled promises.
• Turns some exceptions into fatal errors.
• Adds private and public to all class properties and methods.
• Removed a ton of dead code.

I did this all by hand. It was painful.

Test Plan

CI. Verify no snapshot changes.

[ematipico]

Should we create a rule that enforces these keywords now? So we won't miss this in the future

[sebmck]

I think we should, but I don't think we could have it enabled by default as this level of explicitness isn't usually necessary or the norm when writing TypeScript and would conflict with a lot of existing code.