That information is stored in the database of the instance you're on. Note that this only affects the UI. It does nothing more than make blocked users invisible for you. They can fully interact with your posts, comments, view your profile, etc.
this post was submitted on 30 Apr 2025
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Your Blocked User list is stored within the instance you're on (for you it's lemmy.ml), and not shared to anyone else. Note that the people you block can see your posts through various ways due to the nature of ActivityPub.
The people banned from communities and instances are visible to all instances. You can see the modlog on lemmy.world as a reference, where moderation from lemmy.ml communities are visible on its modlog.