refactor: polish the promise logic for chat pulling

Description

When working on [VS Code] Update Duo Chat message handling to e... (#1397 - closed) I found some unnecessary uses of new Promise() and Promise.resolve in our chat async code.

This is a small cleanup. It is a pure refactoring, no user-facing logic is changed.

Related Issues

Part of #1397 (closed)

How has this been tested?

I tested that chat still works.

What CHANGELOG entry will this MR create?

• fix: Bug fix fixes - a user-facing issue in production - included in changelog
• feature: New feature - a user-facing change which adds functionality - included in changelog
• BREAKING CHANGE: (fix or feature that would cause existing functionality to change) - should bump major version, mentioned in the changelog
• None - other non-user-facing changes