direct selection tool - unable to shift click to select multiple anchor points

Does the Shift key work at all in InDesign, like multiple-selecting objects and moving them?

If Shift fails altogether, it could be caused by third party software (browser extensions, anti-virus software) which interferes with keystrokes. Reboot your computer, and launch InDesign before any other application. If it works then, the problem is in other problems, and you'll have to check between launching other apps, especially web browsers.

Assuming that you are holding the shift down when selecting it sounds likely that it could be a problem that could occur if you checked the option to import previous settings and preferences that is offered in the Advanced Options during the install. Please see CC 2018 InDesign—Don't Import previous settings and preferences . This post was written for CC 2018 but migrated preferences still seems to be a source of trouble for many and the directions on how to deal with this are still the same. Hopefully, resetting the program back to its defaults will solve your problem.