Selectors and CSS dialog cannot apply class to objects or create or update class from selected object
The Selectors and CSS dialog has a really weird behaviour. Click a class, and instead of applying the class to the chosen objects, it just finds all the existing objects of that class!
I would have figured that left-click would apply the style to the selection, and under right-click you would have a command like “Find all objects using this style”, a command that would also appear as Edit → Select Same → CSS class.
I am not sure how CSS in Inkscape was meant to be used, but the UI does not really show any awareness that CSS exists. That same context menu could also have “Update style to match selected object” so long as only one object is chosen. There is a natural question of how you are meant to edit CSS-based style, as you cannot do it visually. Microsoft Word for example lets you bring the modifications to a style into the style definition, which is what I figured you might get to do from the Selectors and CSS dialog.
Moving inline style to a CSS class can be done with an extension, when this really belongs inside the Selectors and CSS dialog too.
(I’ve largely ignored the benefits of CSS in SVG in illustrations that have different-shape objects with the same visual style, as Inkscape’s UI does not really make it possible to use CSS. The bigger bugbear is the inability to apply style overrides to clones, but I guess that is just another one of the brain-dead “not invented here” SVG limitations like conical gradients …)
Inkscape 1.2.1 (9c6d41e410, 2022-07-14)