I have no idea what ChatGPT told you.
The simplest solution requires vba.

You are using a REF (Cross-reference) field.

1. These do not automatically update.
2. They require that you have a bookmark as the source. You have not bookmarked your source. Bookmarking a CC to reference the result is not simple.

I tried using a copy of a Mapped Document Property instead of the REF field but was not successful. I think I've done this in the past, but not with a DropDown CC.


References:

• Repeating Data (Populating Multiple Like Fields) by Greg Maxey
• Mapped Content Controls by Greg Maxey
• Ref field
• Dealing with Fields in Microsoft Word