The problem is that, if I'm connected directly via wire to the bridge router if I can't access 192.168.2.1 or 192.168.1.21
If, instead, I connect to the main router and I try to connect to the bridge router control panel via 192.168.1.21 it works.
I've also noticed that if I force my wired PC to use an IP address in the form of 192.168.2.x and setting the gateway to 192.168.2.1 I can access the control panel but I'm no more able to access the internet.
I think there's some sort of misconfiguration when it comets to the IP of the bridge router but I can't find a fix
Your configuration is correct and this is the expected behaviour.
The LAN interface subnet will be used only as a “management” interface, as devices connecting to the Wi-Fi repeater will be on the main network's subnet instead. You will have to set your PC with a static address in the same subnet as the LAN interface (like 192.168.2.10 for our example) to connect again to the Wi-Fi repeater's Luci GUI or SSH.
Set your PC's ethernet or Wi-Fi settings at static IP 192.168.2.10 and default gateway 192.168.2.1, then connect again to the wifi repeater (through ethernet or wifi). When you finish all of the following steps, remember to reset your PC's IP address back to the original address (or DHCP), otherwise you won't have Internet access. The repeater won't route traffic from the 192.168.2.0/24 subnet.
No, you can. You can add more IPs on the network interface of the client. So you can have the usual 192.168.1.X for internet browsing and the 192.168.2.Y for the management. Don't add gateway/dns for the 192.168.2.Y though.