If you open up new windows in Opera (ctrl + n) and goto the site you want in each, move the windows to the monitors you want and close Opera by clicking the menu button at the top left of Opera and choosing exit, when you start Opera again, all those windows and tabs should be restored to where they were. Of course, any other tabs and windows you have open will be restored too. If that's not what you want, you'd have to close any extra tabs and windows besides the ones you want before doing menu -> exit. Just make sure you have "Retain tabs from the previous session" set at the URL opera://settings/onStartup.
If you're using Opera GX, you can goto the URL opera://settings/profiles and create extra profiles. You can then open those extra Operas and move each to the monitor you want. When you close and open them back up, they should go back to the monitors they were on. Also, in each of those profiles, you can goto the URL opera://settings/onStartup and set them to open a specific page on startup.
For regular Opera (Opera One), you can create extra profiles this way.
Besides those ways, there might be a session manager at https://chromewebstore.google.com/search/session that can do what you want.
Or, you could do something weird like create:
loadopera.bat
cd "%localappdata%\Programs\Opera"
opera --new-window --window-position=0,0 --window-size=640,480 "https://www.google.com" | opera --new-window --window-position-100,100 --window-size=640,480 "https://example.com/" | opera --new-window --window-position=200,200 --window-size=640,480 "https://vivaldi.net/" | opera --new-window --window-position=300,300 --window-size=640,480 "https://opera.com/"
and then double-left-click loadopera.bat to start Opera.
If you want the windows to open maximized, you'd remove the --window-size switches. Due to a bug in Opera though, they'll open maximized anyway even with --window-size set.
For getting them on the monitors you want, you'd edit --window-position for each and change the x coordinate (the first coordinate) to enough pixels to get that window on the screen you want. That's assuming you have things to expand across all monitors.
