Probe connectivity to the configured git remote

Probe the configured remote with the stored bot key (SSH ls-remote, no clone). state ∈ connected|auth_failed|host_verification_failed|unreachable|error|not_configured. auth_failed is expected until the key is registered, and its "message" says where it belongs for this provider — which differs on Azure DevOps. "unpushed" lists local branches whose tip has not reached the remote, oldest first, with age_seconds — a non-empty list means writes are not durable even though state is connected. Admin only.