From previous experience of both setting up and managing Wi-Fi extenders, my understanding from carrying out scans of the 2.4/5GHz bands is that each extender broadcasts its own SSID - however, I'm less familiar with consumer mesh systems. Assuming that a mesh was set up that included 4 nodes, would carrying out a scan at the time the mesh was running show a single SSID or 4 separate SSIDs all broadcasting the same name?
No, the purpose of a mesh system is to use a common SSID (so clients can roam.) The nodes do have distinct BSSIDs. In fact, an access point may have multiple BSSIDs if it has more than one radio and/or serves multiple SSIDs to separate clients into different groups / WLANs.
Juniper has a good explanation.