Which AP mode allows client traffic to break out locally at the branch and provides AP survivability during a WAN outage?

FlexConnect with local switching enabled is the correct answer. This mode allows client data traffic to be switched locally at the branch office AP, rather than tunneling back to the central WLC. This is crucial for survivability during a WAN outage, as clients can still access local network resources even if the connection to the WLC is lost. It also reduces WAN bandwidth consumption. Lightweight with local switching disabled means all traffic tunnels to the WLC, which would fail during a WAN outage. OfficeExtend is for remote workers, not branch offices, and focuses on secure tunneling to the corporate network. Local mode always tunnels traffic to the WLC, making it unsuitable for WAN outage survivability.