I've got it working completely. Here's a screenshot of the settings I've added. One thing to note is that you must specify the Sql environment variables and the path's must match that of the container path.
ASPNETCORE_ENVIRONMENT=Production
ASPNETCORE_HTTP_PORTS=5000
Remotely_ApplicationOptions__DbProvider=SQLite
Remotely_ConnectionStrings__SQLite=Data Source=/app/AppData/Remotely.db
The author also mentions "I did not test with Cloudflare Tunnels, so I'm assuming that still won't work." but it's working fine for me.