Can an iPhone Use an HTTP Proxy on Cellular Data?
The proxy setting for one Wi-Fi network does not extend to cellular data. Managed devices have a separate Global HTTP Proxy payload.
Turn off Wi-Fi and the proxy setting seems to vanish. On an iPhone configured through a Wi-Fi network's HTTP Proxy screen, that is the expected scope: the setting belongs to that Wi-Fi network.
It is not a general cellular proxy field. Re-entering the same address under another saved Wi-Fi network will not change the phone's cellular route.
Managed iPhones have another option
Apple provides a Global HTTP Proxy payload for managed deployments. Its deployment guidance describes a configuration applying across Wi-Fi, cellular, and Ethernet, with supervision required on iPhone and iPad.
This is an organizational management feature, not a hidden switch that any arbitrary configuration profile can unlock on an unmanaged phone. Check the supported enrollment and supervision requirements for the device.
“Global” still needs a traffic definition
Global HTTP Proxy concerns web traffic. It is not a promise that every protocol becomes an HTTP proxy request, and it should not be described as a full-device VPN merely because it applies across network connections.
An automatic configuration can also contain bypass decisions. The management payload has options relating to unreachable PAC files and captive-network access; those affect when a direct connection may be allowed.
For an organization, the practical questions are whether the device is eligible, whether the proxy is reachable from a mobile network, and which traffic the chosen arrangement covers. For a personal device, use an application's supported proxy option where available or choose a supported network service for the required traffic scope. Do not install an unfamiliar management profile simply because an old forum answer says it changes a proxy.