Apply Same Text Style to Multiple Documents

I have a lot - 3500 - rich text documents that I want to apply the same text style to. The style is called The List.

Ideally, I would select the docs, start the script, and it would go through each of the files and apply the Text style.

Can anyone show me where to begin?

AFAIK rich text styles defined by the user can’t be applied via AppleScript. But it should be nonetheless doable, see for example ~/Library/Application Support/DEVONthink Pro 2/Scripts/Format.