Please check the following registry key:

https://docs.microsoft.com/en-us/dotnet/framework/migration-guide/how-to-determine-which-versions-are-installed

Does it indicate that perhaps .NET Framework 4.7.1 was recently installed along with the latest Windows Updates?  If so, .NET Framework 4.7.1 is known to cause issue with K2 version 4.7 and a patch is available.

The application of the November CU + FP5 or later:

https://help.k2.com/kb002132

Had a look at this yesterday.  Release is 394271, which equates to .NET Framework 4.6.1.

I've attached the complete diagnostic build output if it's of any help.

This was located in the logs, however not sure if it is related yet:

Could not resolve this reference. Could not locate the assembly "SourceCode.HostServerInterfaces, Version=4.0.0.0, Culture=neutral, PublicKeyToken=16a2c5aaaa1b130d". Check to make sure the assembly exists on disk. If this reference is required by your code, you may get compilation errors.

Is this purely a client tools machine?  If so, perhaps we can just try a Repair of K2 blackpearl, a Repair of K2 Smartforms, and re-application of the CU/FP on this machine.

I assume the same issue is not experienced on another client tool machine connecting to the same server or from the server (if visual studio is somehow installed there).