Microsoft has chosen not to port Visio to the MacOS.
The only effective way is to run a Windows Visio version on your Mac via a Parallels Win10 VM.
In other words, you need a licensed version of both Visio and Windows along with the Parallels application. You''d then create a Windows Virtual Machine (VM) on your Mac and install Visio in the VM. It works.
I currently run High Sierra on my Mac. With Parallels, I also run WinXP, Win10 and Big Sur VMs. I've installed Visio, Photoshop CS6, MS Access, etc. onto WinXP. Works like a champ and no subscription as they are older 2007 licensed versions. I run other Windows only apps in the Win10 VM. Seamless operation between the Mac and Windows.
FYI - For WinXP, it is installed with no interface to the internet and I run only the apps mentioned. I only exchange files with my Mac and to my printer. WinXP is no longer supported by MS, but I only need it principally for Visio and CS6. However, I rarely use CS6 (Photoshop) as I've switched to Affinity Photo on the Mac.
If the WinXP or Win10 VMs ever got infected, it takes a few minutes to reload them via Parallels. They are actually a large file each which are backed up by TM and CCC. No need to ever reinstall Windows from scratch.
OK, downside other than the subscription to Visio, you need to purchase Win10 and Parallels. But if you have Visio files, its the only path other than buying a PC.