To be clear, the conflict is likely between the disparity in versions you are trying to run. I'm unable to install Visio 2016 alongside my Office 365, so I've created a VM HDD to run it with no issues - hope this helps?
@Jacket …You can not built a old house on a new one....so if you want to install visio 2013 first uninstall office 2021 or just download Visio 2021 version and you are good to go