How to "Put Back" multiple files from trash back in to their respective folders?

You should be able to select multiple and "Put Back." However, if any of the ones you have selected cannot be "Put Back," then it won't give you the option to put the rest back.

Why an item can't be put back is likely difficult to determine.

To clarify @Barney-15E's answer: You can right-click or Control-click on the selected file(s) and select "Put Back" from the pop-up context menu. One of the options on the menu bar may also have the "Put Back" option as well.

If you don't get the "Put Back" option as @Barney-15E mentions, then select fewer files or do them one at a time.

Try opening the trash, selecting the files, then dragging then to where you want them.