I was just commenting about how it’s half-assed design to just slap an existing icon against a white background and call it a day. Compare to the lawnchair icon, locus, or even the Lyft icon in your screenshot. You find the names annoying, I find the design laziness annoying. Companies do it on iOS as well (including Apple).
Possibly save Facebook website as a web app.
I’m not sure though if the data is siloed from the rest of Safari on iOS. You could also try downloading a third party browser from the App Store and using it exclusively for Facebook.
I guess one way to test this would be to:
If so, then it’s more likely cookies, etc aren’t shared between the two.