How do I unlock reactions?

Solution 1:

These expressions seem to be called reactions. Searching for that found me the following 'guide' from Playerzdominiance:

They are achieved little by little, as you progress through the game. Once you have unlocked the Nook store, Tom Nook will tell you that 3 inhabitants want to come and settle on the island. Then you will have to build a bridge. From there, one of your residents will go talk to you and teach you how to use these expressions. To unlock other gestures, you must talk to the rest of the locals during the adventure. As you walk silently around your island, some animals will exclaim your name and run towards your character. Talk to them to learn a new emote.

(emph mine). Other sites also confirm this. So talk to any villager that calls out your name, and you will learn new reactions.