There should be an option in Visual Studio Code to pin tabs, like you can in Visual Studio.

As with issue #10739 there should be a config option allowing you to hide the "pin tab" icon in the tab itself if you just want to use the right-click menu or shortcut to pin/unpin tabs.

There should also be an option (again, like in Visual Studio) where pinned tabs are put onto a separate line above the other tabs.