Hi AlaskanAvalanche,
Have you checked the Mobile Data setting for Safari as suggested in the post you referenced? From the support article View or change cellular data settings on iPhone those steps are:
"Set cellular data use for apps and services
Go to Settings > Cellular, then turn Cellular Data on or off for any app (such as Maps) or service (such as Wi-Fi Assist) that can use cellular data.
If a setting is off, iPhone uses only Wi-Fi for that service.
Note: Wi-Fi Assist is on by default. If Wi-Fi connectivity is poor, Wi-Fi Assist automatically switches to cellular data to boost the signal. Because you stay connected to the internet over cellular when you have a poor Wi-Fi connection, you might use more cellular data, which may incur additional charges depending on your data plan. See the Apple Support article About Wi-Fi Assist."
Is yours set to enabled, or changing as that post described?
It's also worth checking into VPN or security software settings to determine if there are any impacts specifically to Safari if you use either of those options. Consider also if you use About iCloud Private Relay disabling that temporarily for testing purposes.
Regards.