You need to left-click in the search box (you should see the blinking caret) before you right-click + paste. Otherwise it doesn't work and you get the System restore/resize options.
I do that, and I see the blinking cursor:

Taking a screenshot unfortunately does not include the mouse pointer.
However, if I left-click the search box first, then I get no popup menu at all when I right-click, even when the search box has input focus.
It does appear as though KB4532695 has resolved the primary Explorer Search Box issue. But this problem of the context menu not showing correctly on right-click or not at all, while not breaking the search functionality, does present a usability problem
that should not exist.
One would expect at the very least that when a user performs a right-click on the search box that it would receive input focus and then immediately display the appropriate context menu with
Cut, Copy, Paste, Delete, Select All commands.
In the above Windows 7 Screenshots (from WMWare Workstation), it can clearly be seen that the main file list has input focus, and that the context menu displays immediately upon right-clicking the search box, without the requirement of first left-clicking.
This is I think also the search box behavior expected from Windows 10 users.