Cannot run Sql Server Agent jobs with PowerShell script
It sounds like you have a good way to reproduce the problem:

xp_cmdshell 'PowerShell.exe $PSVersionTable'

The next step I'd take is to do some tracing to determine where the error is happening. Since you aren't getting a stack trace in your repro, I'd start by running Process Monitor.

I'd want to start by filtering on processes named Powershell.exe, and then adjust the filters based on the data captured. My suspicion is that this will turn out to be a problem with the PowerShell profile for the Windows service account, but hopefully with Process Monitor you'll get an idea of what error is leading up to the generic -1073741819, which is defined as being a default or unknown error in various Windows libraries.

Significant edit: According to the Visual Studio ERRLOOK feature, the error message of -1073741819 shown in the lower-right corner of the stack trace in your post translates to 0xC0000005. This is defined as STATUS_ACCESS_VIOLATION in ntstatus.h. It could be that some component is not correctly installed, or something is interfering with it (e.g. antivirus). If an access violation is occurring, there might also be further details in Windows' application log.

I'd suggest testing running Process Monitor in a non-production environment first until you feel familiar with it, and selecting the 'Drop Filtered Events' option to avoid consuming large amounts of memory from buffering all events.