fix: set SSH key ownership to container user with mode 600

- Mount SSH keys as bind (not ro) so docker exec --user root can chown
- Add apply_ssh_permissions() to permission_fixer.py
- Call apply_ssh_permissions() after container start for all instance types
- Derive container user from home_dir (/root → root, /home/user → user)
- Tests: apply_ssh_permissions unit tests + start_instance integration tests

Quality gates: pytest 236 passed (6 pre-existing failures), tsc --noEmit clean

apps/api/src/services/permission_fixer.py

@@ -104,6 +104,69 @@ def apply_mount_permissions(
     return results
 
 
+def apply_ssh_permissions(
+    container_id: str,
+    ssh_target: str,
+    container_user: str,
+    timeout: int = 10,
+) -> dict[str, Any]:
+    """Fix SSH directory ownership and permissions in a running container.
+
+    Runs chown and chmod on the ~/.ssh directory so the container user
+    can use the keys (SSH requires the private key to be owned by the
+    user with mode 600).
+
+    Args:
+        container_id: Docker container ID or name.
+        ssh_target: Absolute path to the .ssh directory inside the container.
+        container_user: The container user that should own the keys.
+        timeout: Max seconds per docker exec command.
+
+    Returns:
+        Result dict with keys: success, error.
+    """
+    result: dict[str, Any] = {"success": True, "error": None}
+    try:
+        # Ensure directory is owned by the container user
+        _run_in_container(
+            container_id,
+            ["chown", "-R", f"{container_user}:{container_user}", ssh_target],
+            timeout,
+        )
+        # Set directory permissions
+        _run_in_container(
+            container_id,
+            ["chmod", "700", ssh_target],
+            timeout,
+        )
+        # Set private key permissions
+        _run_in_container(
+            container_id,
+            [
+                "sh",
+                "-c",
+                f"find {ssh_target} -name 'id_*' -type f -exec chmod 600 {{}} +",
+            ],
+            timeout,
+        )
+        logger.debug(
+            "Applied SSH permissions for user %s on %s in container %s",
+            container_user,
+            ssh_target,
+            container_id,
+        )
+    except PermissionFixError as exc:
+        result["success"] = False
+        result["error"] = str(exc)
+        logger.warning(
+            "SSH permission fix failed for container %s (target=%s): %s",
+            container_id,
+            ssh_target,
+            exc,
+        )
+    return result
+
+
 class PermissionFixError(Exception):
     """Raised when a permission fix command fails."""