Is it possible to Automatically assign Extender Mode to an specific wifi/BSSID only? (Beryl AX)

Interesting remark.
But normally with extender in 802.11 wifi connection, all devices behind the extender use the same MAC address of the extender for the wifi connection (One MAC address & multiple IP addresses.) Exceptions on that are "WDS, bridge mode, mesh". But these last 3 are not always working between different brands.

Other solution is to make a tunnel between the 2 wifi devices.
It then has to be a Layer2 tunnel (L2TP, Zerotier, VXLAN, PPTP-BCP, EOIP,MPLS/VPLS...). Zerotier is a very nice one, and will eliminate all intermediate routers of Zerotier-world-network when it can. And here it will be a direct connection.