I think the check in check out process without the eclipse plug-in is tricky to deal with.
You could "try" to checkout Team->share
the UI5 app in eclipse. Then export
the project using file
level export tool.
From there edit with VS code.
Import back in or manually include changes back into Eclipse.
Then using eclipse to check into SAP Backend.
Unfortunately accessing directly from Se80 in backend there is no export / import tool for files except for mimes. So unless you know how to call the plug-in interfaces, you would be creating or changing files and pasting code manually.
Writing the VS code plugin to do the check in and check out isnt impossible,
but the eclipse plugin uses rest and SAP proprietary RFC calls. Ive not seen docu on the interfaces. They may be internal only.
Its not easy to recommend what you are trying.