> I wonder what iOS Edge does which iOS Safari doesn't do
Being a "Managed App" through MDM/Intune. Typically it's used when installing corporate apps in a BYOD scenario. The managed apps are isolated from information sharing with unmanaged apps, e.g. policies can be applied preventing copy/paste, access to Files.app, etc. It (and it's isolated storage) can also be remote wiped without nuking the whole device. Edge.app still uses the Safari rendering engine, etc. like is generally the case with 3rd party browsers on iOS.
You can't do this with Safari.app unless the whole device is managed, which doesn't work well for BYOD.
We have this policy at work and it’s infuriating. I had to install edge once to access some work resource and immediately uninstalled it. I can’t even access our GitHub without it, even through the official app.