Yes Indeed the ISP is the same for my home and my basement so I have 2 links from the same ISP but with different IPs, for the basement, I'm using public IP, and for the home internal. But both are provided by one ISP.
Ah, it wasn't obvious from the description (althoung the mentioning of the gateway being the same device for both uplinks should have rung a bell). So if the ISP is ready to bridge some VLANs between your two uplinks, you can indeed enable vlan-filtering
on the LAN bridge, make the WAN interface just another VLAN on that bridge, set the uplink interface as an access (untagged) one for that "WAN VLAN" and permit the VLANs you want to extend from home to the basement on that interface (all of that on both your devices). And you have to coordinate the VLAN IDs between your two routers of course. The ISP may tell you which particular VLAN IDs to use, and maybe they will even tell you to keep the WANs tagged as well.
There is a great article on VLANs here
. The debugging may be a bit of a challenge, but as your ISP is so flexible that they have offered you the VLAN approach (larger ISPs usually avoid anything that doesn't fit to their pre-defined products), they should be able to cooperate well. And of course you can come back here if something doesn't go as expected.