feat(participant): Report errors to telemetry VSCODE-605

[nirinchev]

Description

This reworks a little the error handling in the participant to streamline error reporting. It's now wrapping the entire chat handler rather than only the code that invokes the model.

Additionally, we're now showing the welcome message at all times, even if the prompt was empty.

Checklist

• New tests and/or benchmarks are included
• Documentation is changed or added
• I have signed the MongoDB Contributor License Agreement (https://www.mongodb.com/legal/contributor-agreement)

Motivation and Context

• Bugfix
• New feature
• Dependency update
• Misc

Types of changes

• Backport Needed
• Patch (non-breaking change which fixes an issue)
• Minor (non-breaking change which adds functionality)
• Major (fix or feature that would cause existing functionality to change)