The contextual sections variant of the notebookbar deals a lot with styles. Among others the table style is such a basic function made salient by a big button. However, the actual table styles in this menu are only dummies. So what we need is a list of recently used table styles filled with some items by default. For example we define Blue, Yellow, Red, and Green as default styles resulting in a menu with these items. When the user chooses another table style like Brown the last item from the list is removed and the new one inserted as first.
You have to decide which of the available table styles you want to include in the drop down menu, set the drop down menu control to be a svtlo-ManagedMenuButton control and then add uno commands similar to below into the menu entries.
Note that bug 137067 complains that svtlo-ManagedMenuButton is not GTK welded, so it looks out of place.
Pressing "Table Styles" now opens the table styles dialog, where one can chose from the available styles. No Dummy entries seen anywhere. WORKSFORME
The "Styles" button lists a few entries without any function. It is supposed to work like paragraph styles giving access to some presets and user defined / used styles.
I'm okay if we decide to not realize this NB. Although it would be a pity to just follow what others do.