The mobile version of Pokémon Home for Apple iOS and Android have been updated to version 1.2.1 and new filter features have been added and some bugs have been fixed.

What’s New

• Improved search result filters for the GTS "Search for Pokémon" function.
• The "Include people searching for Legendary and Mythical Pokémon" option has been updated to "Include people searching for Legendary, Mythical, and other special Pokémon."
• You can now filter your results based on what Pokémon you have deposited in Pokémon HOME.
• Added the ability to place multiple Pokémon in the Wonder Box at once.
• Revised Challenge completion messages for improved clarity on what Challenge you've completed.
• Added the ability to view Pokémon's Natures under Pokémon Rankings in Battle Data. (If a Trainer used a mint on their Pokémon, the Nature shown will correspond to the mint used.)
• Added a Back button to Battle Data screens.
• Fixed the issue where Toxtricity's Gigantamax form would not be displayed in your Pokédex.
• Added new informational feature.
• Made various other fixes.

Sources: https://play.google.com/store/apps/details?id=jp.pokemon.pokemonhome and https://apps.apple.com/us/app/pok%C3%A9mon-home/id1485352913