The key attributes are ipv.nat=false,in which the virtual machine can access the host, but cannot access the host gateway 192.168.1.1 and www.google.com.
The reason why I set ipv4.nat=false is to use Incus’s BGP technology,here are the settings for my incus cluster
Incus is advertising its network to your FRR router, that router received the route and properly put it in its routing table, allowing it to reach the instances running on Incus.
It sounds like your FRR router isn’t your primary router though, as that is at 192.168.1.27 whereas your primary router likely is at 192.168.1.1.
So your problem seems to be that your primary router itself isn’t aware of that 10.1.22.0/24 subnet and how to route to it, which is then why your VMs can properly interact with their host as well as with 192.168.1.27 but not with 192.168.1.1 or anything behind it (the global internet).
Your BGP router doesn’t do anything as far as I can tell.
It does receive the routes from Incus but because it’s not the actual router for your network, it knowing the route to Incus doesn’t really do anything. You need your actual router to know how to route to Incus.