To the core, the interworking function is an access network — not a core element. That is the shift from earlier Wi-Fi interworking, where the gateway (the ePDG, in the 4G core) sat inside the core itself. Treating the function as access means the same procedures run over Wi-Fi as over the radio: one registration, one authentication, one way to manage sessions.
A device registers through the AMF and is authenticated by the AUSF with 5G credentials — EAP-AKA′ or 5G-AKA — exactly as a cellular device would be. Before registration completes, an IPsec security association is established between the device and the interworking function, and from that point the NAS signalling, both mobility and session management, travels inside it.
Sessions follow the same path. Over that signalling association the device runs NAS session management with the SMF, via the AMF, to establish a PDU session. For each session the function sets up IPsec child associations — one per QoS flow — toward the device, and a GTP-U tunnel toward the user-plane function. User data then rides inside IPsec between device and function, and inside GTP-U between the function and the UPF.
The reference points are worth knowing, because they name every leg of that path: NWu is the secure tunnel between device and function; Y1 and Y2 sit on either side of the Wi-Fi access point; N1 is the NAS link to the AMF, N2 the control-plane link from the function to the AMF, and N3 the user-plane link to the UPF.
Because the function behaves like access, a device can hold PDU sessions over the radio and over Wi-Fi at once, and move a session between them — the basis for offloading to Wi-Fi without losing identity or policy. A few things do not carry over, though: over untrusted Wi-Fi there is no paging, no mobility registration and no periodic registration, so the patterns that rely on the network reaching a sleeping device simply do not apply.