Please keep in mind that the 64-bit version of Microsoft Access Database Engine 2016 Redistributable should only be installed if you do not have ANY 32-bit Office products installed. This will also cause issues in other Office suite products, such as Excel, Outlook, Word, etc.
I have ArcGIS Pro installed on one of our servers to process nightly scripts with only 64-bit version of Microsoft Access Database Engine 2016 Redistributable installed - No MS Office installed. I can utilize .accdb and .xslx files without any issues. However, I cannot access these files on our desktop systems with 32-bit Office installed. Fortunately, we have licensing to both versions and IT installed the 64-bit version of Office when ever we install ArcGIS Pro.
A possible third option, would be to generate a script that would run on a regular basis to import your Access database (or selected tables) into file or enterprise geodatabase tables.
Best of luck...