feat: improve log context details

What does this merge request do and why?

This MR improves the context details of logging, which includes:

• Add language_server_version, workflow_stop_reason and workflow_last_gitlab_status fields to the log line.
• Centralize exception logging via log_exception, which allows us to cross-join the request logger and exception logger to extract the characteristics of the failures.

Related to https://gitlab.com/gitlab-org/modelops/applied-ml/code-suggestions/ai-assist/-/issues/1393+ Improve structured logging on DWS (#1484) Add metadata to metrics and events (#1571)

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

Merge request checklist

• Tests added for new functionality. If not, please raise an issue to follow up.
• Documentation added/updated, if needed.
• If this change requires executor implementation: verified that issues/MRs exist for both Go executor and Node executor or confirmed that changes are backward-compatible and don't break existing executor functionality.