A problem with Pages

The only application on earth that can open a Pages document is Pages. There is no problem with Pages per your post. Since macOS has no automatic pointer focus when switching between applications, one must choose among these options:

• Move the Pages document window (assuming you have done the merge windows) to another area of the screen.
• Use the Finder's cmd+Tab to switch from Pages to the other application focus.
• Click on the chosen application window to make it frontmost over the occluding Pages document window.
• Click the yellow traffic light on the Pages document's title bar to collapse that Pages window to the Dock.
• Run fewer applications and/or quit those currently unused to reduce window clutter on that 27-in iMac.

There can only be one instance of Pages running, and it can have multiple documents open in separate windows owned only by the Pages application.

If you have multiple Pages documents open, you can merge these into document tabs in the main Pages window via the Pages Window menu > Merge All Windows. One can move to the next document tab with control+tab or the previous document tab with shift+control+tab.