How to move a file to another folder in VS Code?

You can use drag n' drop to move the file

Move is available by right-clicking the file in the sidebar after installing File Utils from the Visual Studio Code Marketplace.

You can also move file with using console (for example PowerShell or Git Bash) in Code.

Recently I have I habit to move files or folders in sidebar, via ctrl + x (cut) and ctrl + v (paste), after this action Code automatically updates imports.

Drag & drop method also works.

The OP issue 1043 which was resolved with VSCode v1.37 (2019)

That feature is still improving, with issue 98309: "Support multiple files in working copy file service".
See PR 98988 "File operation events support multiple resources"

That allows other files which depends on the move to be properly updated when you are moving several files.
That will avoid this: