For one thing, you need to bridge your 2nd router and disable its DHCP server, effectively making it an Access Point.
If that’s not enough to address your issue, you could also try setting the Wifi SSID and password the same, provided its set to use different channels than your main router, although this can make it a pain to force a device to switch from one router to another. (my second router also has a separate SSID partially because the one for the kids’ devices and living-room TV shuts off for bed-time).
End of the day, unless you have commercial routers/APs or Mesh routers that are setup to inerroperate on the same SSID while using an Ethernet backhaul, there’s going to be quirks and compromises.
Or if OP really can’t do that (that’s by far the best solution), KDE Connect also lets you hardcode some IPs it’ll try to connect to. Given the computer is on the main network, using the IP of the computer directly would make it work fine behind the second router.
But ideally, they really should be the same network.