chore(core): fix typing issues

[Archento]

Proposed Changes

This PR addresses a lot of typing inconsistencies and aims to fix Pylance and Pyright warnings. It also fixes fetching the correct protocol on creation of the ExternalContext within _process_message_queue() and the odd typo and missing doctoring.

Types of changes

• [x] Bug fix (non-breaking change that fixes an issue).
• [x] New feature added (non-breaking change that adds functionality).
• [ ] Breaking change (fix or feature that would cause existing functionality to stop working as expected).
• [x] Documentation update.
• [ ] Something else (e.g., tests, scripts, example, deployment, infrastructure).

Checklist

• [x] I have read the CONTRIBUTING ↗️ guide
• [x] Checks and tests pass locally

If applicable

• [ ] I have added tests that prove my fix is effective or that my feature works
• [x] I have checked that code coverage does not decrease
• [x] I have added/updated the documentation