feat: add SSH connectivity check

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/autossh_mgr/check.py

@@ -0,0 +1,24 @@
+import os
+import subprocess
+from autossh_mgr.config import TunnelConfig
+
+
+def build_ssh_check_cmd(tunnel: TunnelConfig) -> list[str]:
+    return [
+        "ssh",
+        "-o", "BatchMode=yes",
+        "-o", "ConnectTimeout=5",
+        "-i", os.path.expanduser(tunnel.identity_file),
+        "-p", str(tunnel.port),
+        f"{tunnel.user}@{tunnel.host}",
+        "true",
+    ]
+
+
+def check_connectivity(tunnel: TunnelConfig) -> tuple[bool, str]:
+    result = subprocess.run(
+        build_ssh_check_cmd(tunnel),
+        capture_output=True,
+        text=True,
+    )
+    return result.returncode == 0, result.stderr.strip()