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My (perhaps naive) understanding is that Electrum sends first n addresses to a single randomly-chosen public server to check balances.
If all addresses have balances, Electrum then sends next n addresses (and so forth).
Are all above requests sent to same single randomly-chosen public server?
If so, this means server can infer that all addresses are owned by same wallet.
From docs:
One of the servers, arbitrarily, is selected as the “main” server.
The client subscribes to its own addresses (nit: sha256 hashes of scriptPubKeys) so that it would be notified of new transactions touching them. It also synchronizes the existing history of its addresses. This means the client sacrifices some privacy to the server, as the server can now reasonably guess that all these addresses belong to the same entity.
