Even though the emojis are not embedded in your public profile description, you can copy and paste them from these lists. You can directly copy and then paste the emoji where you want it (or you can write the code, if you want).

Some emojis might not work. After you publish your profile, you will see question marks where the emoji should have been. There is no fix for it, just to replace the emoji with a different one.
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Example of emojis not working: