Sorry to read that this hasn’t sorted itself out yet.
It sounds like your iPhone settings are all good.
Yes, in this situation you only require Bluetooth for your Fitbox Gate to communicate with your PC.
And yes, according to Zwift’s support pages, you should still be able to sync Companion to Zwift if your PC is connected to the internet via an Ethernet cable, as long as your iPhone SE2 and the PC are accessing the same network path.
Unfortunately, I don’t have experience of having to do that with an Ethernet-connected device. I’ve seen another thread on this subject that mentions some modem/router set-ups “not allowing traffic between ethernet and the wifi slots”, but I’ll admit I’m out of my depth in this area.
If this isn’t easily resolvable and you want to continue using that PC for Zwift, it might be worth investing in a Wi-Fi USB adaptor for it. They aren’t prohibitively expensive, generally.
In the meantime, for testing/elimination purposes, do you have access to a Wi-Fi enabled device like a laptop or iPad, on which you could run the main Zwift game, to see if Companion syncs up in that instance? (Making sure, of course, to log out of Zwift on your PC first.)
One other thing came to me: are you definitely logged into Companion on your phone using the same Zwift account as the one you are logged into on your PC?