What happens to abilities, stats and levels?
Level:
The Pokémon's level will be the same as its Power Up level in Pokémon GO, rounded down to the nearest integer. This means that Pokémon transported from Pokémon GO can range from level 1 to level 50.
This is what the Power Up level is:
Each Pokémon has a Power Up level that effectively counts how many times it has been powered up. Each level corresponds to a CP multiplier, a value used to calculate the Pokémon's stats and catch rate. Each Power Up increases the Power Up level by 0.5, up to the player's Trainer level + 2.
Moves:
The moves that a Pokémon knew in Pokémon GO have no bearing on its moves in HOME. The Pokémon's moves are reset to moves it would know in the wild at its current level (i.e. its level-up moves at that level).
Abilities:
The Pokémon's Ability is randomly selected from the Pokémon's standard Abilities in Pokémon Sword and Shield.
Height and Weight:
The Pokémon's height and weight are reset to the species' default values. (This is not the case for Pokémon that were transferred from Pokémon GO to Let's Go, then placed in Pokémon HOME.)
IVs:
The Pokémon's IVs are calculated from its IVs in Pokémon GO. In Pokémon HOME, its IVs are equal to one more than twice their corresponding IV in GO (i.e. HOME = 2 × GO + 1). As a result, the maximum possible IV for a transferred Pokémon is 31 (the maximum possible for any Pokémon) while the minimum is 1.
Speed has no corresponding IV in Pokémon GO, so is randomly generated upon transfer.
Sources: https://bulbapedia.bulbagarden.net/wiki/GO_Transporter, https://bulbapedia.bulbagarden.net/wiki/Power_Up
