Is it possible to transfer the Pokemon Sword progress onto Pokemon Shield?

My friend has Pokemon Sword. I played on his console for a couple of hours and made quite some progress.

Now, I want to buy my own Nintendo Switch but with Pokemon Shield instead (so we can transfer the version exclusive Pokemon to complete the Pokedex).

Is it possible to transfer the Pokemon Sword progress onto Pokemon Shield?

The answer depends on how you define progress in a Pokemon game. You cannot transfer your character or any gyms/trials you have defeated between games, but you can trade the Pokemon that allowed you to make that progress so it'll be easy to redo it.

You should be able to trade almost immediately when starting a new game and will just need to catch pokemon you don't care about to trade to your old game. Beware, trading high level pokemon between games can cause them to not listen during battle. This is an old feature since the first games, and they will listen more as you beat more gyms.