I test on my environment, if I install volumn licensed Viso 2016 and Microsoft 365 Apps which uses shared computer activation on one machine, there is no option to change the product key for Visio either.
As I do not have MAK key for a test, I use KMS activation, and here are 2 screenshots.
I think we could install volumn licensed Viso 2016 and Microsoft 365 Apps with shared computer activation on a same machine.
Are the last 5 characters of installed product key shown on your last image the same as the the the last 5 characters of your Visio key?
I suggest you use
cscript.exe "%ProgramFiles%\Microsoft Office\Office16\ospp.vbs" /unpkey:XXXXX to uninstall the product key, and use
cscript.exe "%ProgramFiles%\Microsoft Office\Office16\ospp.vbs" /inpkey:AAAAABBBBBCCCCCDDDDDEEEEE to install your product key for a test.
Please note, according to the artcile "Use the Office Deployment Tool to install volume licensed versions of Project 2016 and Visio 2016", to get the MAK key for volume licensed versions of Visio with the Office Deployment Too, you need to log into the Volume Licensing Service Center (VLSC) and use the key listed under "C2R-P for use with the Office Deployment Tool."
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