It appears as if there is a glitch that people are experiencing that is the same to what you are dealing with; Pokémon transferred from Pokémon Home aren't registering in the Pokedex.
In order to solve this, the you must place the transferred Pokémon into the daycare, and take it out. Despite it being a very odd method, it appears to work, and causes the Pokémon to be registered as caught.
Due to it being fixed by going to the daycare, as stated, it appears as if a bug was made by Game Freak, when it came to registering the Pokémon in the Dex.
I Hope I Helped!
Source 2 (Video)