So nothing to do with the new door.
Everything to do with the new door!
I had some spare time this afternoon, so I did everything suggested above, apart from resetting the router, was going to leave that last.
Batteries reseated, cam uninstalled from app, app uninstalled, then both back on my phone.
Put it on charge, immediately it wanted to pair with the router, so I let it.
While it was charging, it was working perfectly, taking videos of the cat passing in front of the socket

sending alerts to my phone.
After charging, I put the door bell cam back in its cradle already fitted to the door.
It stopped working immediately, I know this because I was making faces at it

No alerts on phone, cam comes up as offline on the app.
A colleague at work had suggested fitting it to the door frame instead of the actual door, she was right, it works perfectly now.
Whatever is inside my new "fire door" (I think steel bars) or the material it's made of (composite, whatever that is), does not let the WiFi signal through.
Thank you all for the suggestions, much appreciated!