Thanks for the detailed report and the screenshots, they made this easy to find.
Your Windows display settings show "1|2" because monitors 1 and 2 are set to Duplicate, so for any application they count as a single screen. That is fine on its own, but it exposed a bug in Zonea: the main menu worked out the "current" monitor from the Windows display number instead of its position in the screen list, and with a duplicated pair (or a disabled monitor, or Windows listing the touch screen first) the two do not match. The wrong button was marked as current and your real one showed as occupied, so no green button was left to click. "Placement" itself is just a label, not a button.
It "fixed itself" after locking the laptop because Windows re-enumerated the screens in a different order, which is pure luck.
This is corrected in the next update, where the monitor buttons always agree with Identify. Until then, if it happens again, change the duplicated pair from "Duplicate desktop on 1 and 2" to "Show only on 1" or "Extend", and the buttons will work.