This lists potential compatibility issues with Microsoft Office, Visio, and Project.

On one machine:
You cannot mix bitness. Office, Visio, and Project must all be either 32- or 64-bit.
You cannot mix Office software installed with different types of installers. All must be Click to Run or all must be Windows (MSI) Installer.

These use only the Click to Run Installer:
Office 365, Office 2019, Visio 2019, and Project 2019.
Office 2013 and 2016 installed from the Office 365 portal.

These use only the Windows (MSI) Installer:
Visio and Project versions 2013 and earlier.
Office 2013 and 2016 downloaded as ISOs.

These use either Click to Run or Windows (MSI) installers:
Visio 2016 and Project 2016

You cannot mix different year versions (2013, 2016, 2019, etc.). Office, Visio, and Project must all be the same year version, with the exception for Office 365 noted below.

Any Microsoft software installed with a Click to Run installer can be installed alongside Office 365. That would include Visio 2019 or later, Project 2019 or later, and the Click to Run versions of Visio 2016 and Project 2016. If you have both Project and Visio installed, their versions must be the same as each other.