iPhone 16e loses internet after restoring backup from iPhone 13

Hi all, I have a weird one for you.

I recently bought a 16E to replace an ailing 13. This afternoon, I set about doing the data transfer; everything was taking ages on the new phone, though the old one and an iPad (as well as every other device) was connecting to the same network just fine.

Finally completed, and the new phone looks like it should - the right wallpapers, passcodes, apps waiting to download... but no downloading. It is constantly throwing out a 'no internet connection' error on that same network - the one everything else is happily working on. But some apps start downloading for a couple of seconds, then stop. I forget the network, try again. Same thing. Eventually even that stops. The restore hangs with about 8/9GB of data waiting to download, as well as all my apps.

I repeat the erase/transfer process a dozen times more over the course of the afternoon, trying both iPhone to iPhone and download from iCloud.

Every time, the same thing happens. Mobile data non-functional, WiFi non-functional. I can't even turn off Location Services when I erase the thing again, because that requires an internet connection.

I've investigated the router, both physically and by logging into it to find out if there are any blocks or limits. There are none.

I erase it again, and skip all options instead. I don't even sign in on my iCloud account. Works perfectly, first time, on the same network it had been failing with all day. I sign in on iCloud; no problems.

Mobile data works; the eSim has transferred correctly.

WiFi works, as if it had never had a problem.

I now have a 16e with nothing on it but my iCloud account, but perfectly working internet, and a 13 with all my data, which no longer has an eSim.

I try to restore the backup, now I know the problem is not the phone itself.

As soon as the backup loads, the internet stops working.

Has anyone else dealt with this nonsense?