VoWiFi (as Wi-Fi calling is called in the 3GPP specs) is similar to VoLTE, but not all SMS go over VoLTE: Unlike for calls, where there's mandatory VoIP in 4G/LTE and beyond (there is no more circuit switching), there's still a fallback path for SMS that uses legacy signalling instead of IMS (which powers VoWiFi and VoLTE/VoNR).

Maybe there are some SMS gateways that are somehow incompatible with some IMS message gateways? (Theoretically, the IM-SM-GW should be transparent to external networks, I believe, but practically I wouldn't be surprised if some weird things lurked in there, requiring a fallback to the signalling path, which is not available on VoWiFi.)

WiFi calling seems to depend on your mobile service provider to provide the service. I guess different networks do it differently.