Options for opened app on the dock doesn't show "Assign to" desktops

I have a work laptop using two external monitors and a personal laptop using one of those, both using Sonoma (14.3 and 14.4.1 respectively, both M1 from 2021, 16" and 15" respectively), but only the personal one shows the option to switch an app window to a different monitor when right-clicked while showing in the dock. And the work one keeps moving some apps' window to a different monitor every time the screen gets locked. How to fix that? It started after I added a Dell monitor rotated by 90 degrees -- exactly the one not used with the personal laptop. But if it's a problem with that monitor, it still doesn't explain the missing option in the dock. What's going on, and how to fix it?