My usage is fairly restricted:

• old school :^) for non-sarcastic irony
• (¬¬) for eye rolling
• shorthand emojis (e.g. if talking about Stardew Valley, instead of “the four hearts event” I might type “the 4♥ event”)
• as a way to avoid a specific word for metalinguistic reasons (e.g. “⟨dog⟩ is the signifier, 🐶 is the signified”)