feat: create extensions/git with manifest, commands, scripts, and auto-install in init

Co-authored-by: mnriem <15701806+mnriem@users.noreply.github.com>
Agent-Logs-Url: https://github.com/github/spec-kit/sessions/809a1dbf-1301-4312-b4d2-e18f9b3e8b2f

extensions/git/commands/speckit.git.remote.md

@@ -0,0 +1,45 @@
+---
+description: "Detect Git remote URL for GitHub integration"
+---
+
+# Detect Git Remote URL
+
+Detect the Git remote URL for integration with GitHub services (e.g., issue creation).
+
+## Prerequisites
+
+- Check if Git is available by running `git rev-parse --is-inside-work-tree 2>/dev/null`
+- If Git is not available, output a warning and return empty:
+  ```
+  [specify] Warning: Git repository not detected; cannot determine remote URL
+  ```
+
+## Execution
+
+Run the following command to get the remote URL:
+
+```bash
+git config --get remote.origin.url
+```
+
+## Output
+
+Parse the remote URL and determine:
+
+1. **Repository owner**: Extract from the URL (e.g., `github` from `https://github.com/github/spec-kit.git`)
+2. **Repository name**: Extract from the URL (e.g., `spec-kit` from `https://github.com/github/spec-kit.git`)
+3. **Is GitHub**: Whether the remote points to a GitHub repository
+
+Supported URL formats:
+- HTTPS: `https://github.com/<owner>/<repo>.git`
+- SSH: `git@github.com:<owner>/<repo>.git`
+
+> [!CAUTION]
+> ONLY report a GitHub repository if the remote URL actually points to github.com.
+> Do NOT assume the remote is GitHub if the URL format doesn't match.
+
+## Graceful Degradation
+
+If Git is not installed, the directory is not a Git repository, or no remote is configured:
+- Return an empty result
+- Do NOT error — other workflows should continue without Git remote information