I have a large set of Google Sheets which have exactly the same Apps Scripts code (several gs files in each Sheet).
Is it possible to update the code of these Sheets with a batch update, instead of opening each Sheet and pasting the new code in each gs file?
No unfortunately, you can't update scripts by using a script.
You can write your master code somewhere and then duplicate the spreadsheet file so all of them will have the same code.
A better approach would be to create your own Library which will contain the full code and all the other spreadsheets will import this library. So you only need to update the code in one place.