Pages app freezes single-click selection until restart

Formally quit Pages and reboot the Mac. Press and hold the shift key while launching Pages. That will cause it to ignore its last saved execution state and may help you avoid any recurring mischief with the application.

Be certain that you are using Pages v14.4 on Sequoia v15.5. I am, and no single-click selects text, it must be a double-click to select a word or a triple-click to select the current paragraph. A single-click is only useful for positioning the insertion beam or selecting a document object (e.g. Text box, image, etc.).

The exception is if you have double-clicked to select a word and want to select additional text after it — then it is a double-click to select the word, press and hold the shift-key, then right-arrow for each additional character you want to select.

All Pages keyboard shortcuts are described in Keyboard shortcuts for Pages on Mac - Apple Support.