You can just click Follow and start following someone. You don’t have to perform a copy-paste dance to bring the username back to your instance and do the following there.
In the Mastodon app you can just click "follow". Since BS doesn't have a web interface at all, it's probably safe to assume that this is not a major reason a BS user would avoid Mastodon. Since they're not on desktop anyway.
When federation is live on the main node on bluesky there will still be some similar effects when you follow links from other servers, in that you'll need to bring that over to your own server somehow to follow and interact.
With Mastodon when you follow another's link you're asked to specify your own instance, in Bluesky you'll enter your domain based username and it will find your instance.
Also with the CDN like BGS caching servers being shared across instances you'll be able to find more content from your home instance so it will feel more like Twitter. You can directly search for users on other servers.