While I don't know about importing entire tilesets with animations for each one, you can add multiple frames at once for each tile set, and you don't need to create separate image files for each one. I reckon that would be easier than your method. Attached a gif showcasing how it is done.
I know I can import multiple animation frames for each tile, but it doesn't help my case.
In your example you have 3 frames for the same tile in one spritesheet, one after the other. It only works fine when your objects are tile-sized (e. g. for my animated volcanoes, windmills and such).
When I'm drawing a river fragment (or seashore etc) I draw a whole image that spans multiple tiles.
Then I add animation to the whole image (e. g. in the attached example I change opacity of the shorelines).
Even to prepare this asset for import I need to run some sort of a script that would pack all A1 tiles into one spritesheet, all A2 tiles into another spritesheet, etc. Then I'll have to import 40 spritesheets each containing 3 frames of one tile.
That's not saving a lot of time, plus I don't have a script that would extract sprites with the same coordinates and pack them into animation strips