I have tested it a few times now and I assume that green iPhone in control center = iPhone GPS and red iPhone = Watch GPS. When I disable Bluetooth but WiFi is still enabled, it shows a WiFi logo instead of a red or green iPhone, so I assume it's then using WiFi to determine the location.
So I think I'll just disable WiFi and Bluetooth in airplane mode and use airplane mode for running.
Normal behaviour (iPhone GPS):
View attachment 1865738
Airplane mode enabled with bluetooth enabled (iPhone GPS):
View attachment 1865740
Airplane mode enabled with bluetooth & WiFi disabled (Watch GPS):
View attachment 1865741
Only bluetooth disabled (location from WiFi?):
View attachment 1865742