Once again appologies for the delay and thanks for providing such useful info in the outputs.
The issue is some confusion that we will clarify in the documentation and also provide better feed back in the CLI.
As stated previously the include paths are not stored in VS, in fact they are dynamically recreated each time a project changes or builds. That is for Vs intellisense.
In Arduino paths are generally worked out dynamically and in this case what is missing is the Arduino Sketch Book folder location. We can see the sketch book location easly in the IDE build output but it is missing from your CLI build output.
For Arduino, the user installed libraries are always assumed to be in "SketchBook\Libraries" which the CLI can't see. This is why you believed include paths are missing.
The reason the CLI can not see the sketchbook is that your CI command does not specify an IDEName (-builder.application_id=) therefore Visual Micro will use the NoIDE option (that you can see in the VsIDE).
In the VsIDE you have specified a Sketch Book folder location of "Public/Arduino/ArduinoGIT" for the "Arduino 1.6/1.8" application but have not set a Sketch Book folder location for the NoIDE application. Hence an unknown Sketch Book location will probably default to "myDocuments\Arduino" where your \libraries do not exist.
1 - NoIDE vmbuild.exe -builder.ide_path="D:\Arduino\arduino-1.8.1" -builder.upload=false -builder.build=true " -builder.verbose=true -builder.verbose_warnings=true -builder.board_id=Pico
2 - Arduino 1.6/1.8 IDE vmbuild.exe -builder.application_id=arduino16x -builder.upload=false -builder.build=true " -builder.verbose=true -builder.verbose_warnings=true -builder.board_id=Pico
Solution Therefore the solution is to either add the optional Sketch Book Location to the NoIDE option in Visual Micro or use the 2nd command syntax example above.
I hope this makes sense?