[FEATURE] GitLab support for Claude Code Slack integration

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

The Claude Code Slack integration currently only supports GitHub repositories. Organizations using GitLab cannot use the Slack workflow to delegate coding tasks by @mentioning Claude.
When invoking Claude Code from Slack, the "Select repository" option only shows GitHub repos, and the documentation confirms "GitHub only: Currently supports repositories on GitHub."

Proposed Solution

Extend the Claude Code Slack integration to support GitLab repositories:

Allow connecting GitLab accounts (gitlab.com and self-hosted instances) in Claude Code web settings
Show GitLab repos in the repository selector when invoking from Slack
Support creating Merge Requests (GitLab's equivalent of PRs) from completed sessions

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

CLI commands and flags

Use Case Example

Use Case:
We're rolling out Claude Code across our development organization. Our codebase is hosted on GitLab. The Slack integration is the most compelling feature for team adoption—developers can stay in Slack, tag Claude with context from bug reports or feature discussions, and get working code without context-switching. Without GitLab support, we lose this entire workflow.

Additional Context

_No response_