Can't use Zerotier one AND Google backup after moving HA to cascaded router

Installation
1

I’ve got a ZTE 4G Modem/Router which I have to use because the provider doesn’t allow me to use any other.
That ZTE thing is -the least to say- not very nice to set up. It can only do a limited amount of fixed IP’s in the DHCP pool and its WiFi is failing every time. (second unit, so I guess it’s a product issue).

I’ve connected a FritzBox 7360 to the ZTE device and configured that as a cascaded router. It works fine, Wifi issues resolved, I can fix IP addresses as I like etc. but there’s two issues with HA:

I’m using ZeroTier for remote access. Once I’m in a different network, I’m not able to get to HA anymore.
When I’m in the same network I can connect to HA using ZeroTier.

Google backup generates errors: Unable to reach token2.habackup.io,
However, when I go into settings and open the Google UI, click re-authorize it works fine (and I can do backups)
Once I leave the UI it logs errors as soon as a backup is scheduled.

The setup worked fine without the cascaded router, so I’m pretty convinced I’m doing something wrong, but I can’t figure out what.

ZTE IP Range: 192.169.0.x
FritzBox IP on the ZTE: 192.168.0.4

FritzBox IP Range: 192.169.0.x

What am I doing wrong?

2

192.169.x.x is not a private network.
Your ZTE network is probably 192.168.0.x with a subnet mask of 255.255.255.0, so you can use 192.168.1.x with a subnet mask of 255.255.255.0 for you network behind the FritzBox.

You should portforward all ports from the ZTE router to the FritzBox, unless the ZTE can be configured for bridge mode. Talk to your ISP about that option.