Update on my situation:
Previous to Microsoft pushing this update that has caused the issue with the persistence of the "Microsoft respects your privacy" pop up, I was running my automations from the Windows Task Scheduler with the option "Run whether user is logged in or not". Today I have returned the automations to working by selecting "Run only when user is logged in".
My best guess as to why this is working is that my logged in user has been able to open Excel, walk through the prompts of the privacy pop up, and Excel remembers my selections. Whatever way that things run when "Run whether user is logged in or not" is checked occurs in the background, and perhaps it is running with a different user or admin/system user that doesn't know which options my primary user has selected for the privacy pop up, and thus keeps prompting for them when my code opens Excel. Even though this is in the background, I can see that the privacy pop up is active after my code errors by looking in Task Manager.
I do prefer to run my tasks as I did before, whether user is logged in or not. Does this added information help anyone understand further what I can do to satisfy the requirements of this privacy pop up so that is doesn't appear again when opening Excel across all users or privileges on my machine?