Enhance diagnostics logging with context-aware timeouts

[adamshiervani]

Summary

• Append diagnostics to log file when supervisor detects a crash

Checklist

• Ran make test_e2e locally and passed
• Linked to issue(s) above by issue number (e.g. Closes #<issue-number>)
• One problem per PR (no unrelated changes)
• Lints pass; CI green
• Tricky parts are commented in code

[IDisposable]

I usually use a coalescing helper (in a utils package) for this

func orBackground(ctx context.Context) context.Context {
	if ctx == nil {
		return context.Background()
	} else {
		return ctx
	}
}