According to the documentation for the SQLVSS Writer service, the account need to be LocalSystem. Not a domain account. I understand that you might want to know why that is, but sometimes we just have to accept that MS documents some requirements and we will have to follow those requirements.
You can of course send a request to MS and ask them to relax this requirement and/or be more specific in the documentation, but I doubt you will have much success, to be honest.
The question is why you insist to not use Localsystem ? Is there a problem with using LocalSystem in your environment?
If Veeam suggest that you should use something else than what is supported by SQL Server, then that Veeam article should be corrected.