Try to explicitly set the URL as https://<url>:443.
EDIT: I can't remember if this will specifically address your problem, but there was a recent situation I recall (involving QR codes) where the app would only recognize URLs with an explicit port.. That might have been fixed already, even, but thought I'd mention it as a quick thing to try.
Do you have their authentication on the tunnel or is it just a reverse proxy with no extra authentication? If you are using their zero trust stuff, it won't work.
If you are just trying to access your stuff remotely, give tailscale a try.
I am trying the same thing except I am using the regular ignition 8.1. I am running the ignition docker version at my home for testing. I setup the cloudflare tunnel and connects fine. I can load the gateway admin and login. I can bring up my app login on same browser, enter my credentials then something weird is happening. The loading page gets stuck and looks like this:
Its stuck on the "Initializing client..." Authenticating .... and stops there.
what is causing the load screen to hang. I would think since the rest is working this should also. On my local machine ignition is on 8089 that gets mapped to the internal docker port of 8088. Cloudflare is http to the my local ip address on my computer using port 8089.