I have a document with many tables, mixed with titles and notes not inside the table but separated by paragraph returns.
If I select the whole document to assign a Table Style the options are grayed out.
If a select only the items of the table (Editor) or the Table (Screen) the style may be applied.
But it ask to manually check one by one?
Someone could write a script, I imagine, to do such a thing. It's not available in the InDesign interface to apply to styles to multiple tables at a time.
Great that you found that answer so quickly. I try never to say something can't be done in InDesign because scripting can offer so many other possibilities.