Ubuntu
1st Monitor 48" UCB-C set as primary
2nd monitor 24" HDMI Brave starts here even when switched off
Chrome starts correctly on Primary window
Are you using the lates Brave build at this time?
Can you try turning both monitors on, launching Brave, dragging the window from the secondary monitor to the primary one, then turning off the secondary monitor with Brave still open – the browser should remain on the primary monitor.
From here, close and relaunch the browser without enabling the secondary monitor – does the browser still try to launch “off screen”?