I've learned some things about the rest of the Pokémon Home pokédex. You cannot trade pokémon of a mythic tier with anyone but a friend. No GTC, no wonder box. So any of the pokémon that can only be gotten from events like trade shows or the world championships, you can only trade from person to person. This will make trading my Jirachis a little harder, but as I found out you can use Jirachi in Pokémon Sword & Shield, and they are a very competitive pokémon, I'm hoping that works in my favor.
So wish me the best of luck and I'll update as soon as I can with the next big step in my journey to catch all the pokémon that are out there.