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For anyone who is still having issues, I FINALLY got the Tea, Tiramisu, and Cake.
For the Tea: Eventually one of the visits to the Rose Garden will trigger it. Just keep trying.
For the cakes: The 2nd NPC (the one standing right outside the cafe) is the one who will prompt asking if you want to try it. You CAN get both the same day, however, they seem to not always have a good chance of showing up. Your best best is to save and exit out of the game, load it back up, and see if they are there. They should eventually show up, but you can play for hours and not see them. It took me about 3-4 resets for each.