Assuming we set aside the fact that public keys and balances are stored locally in plaintext, considering only the perspective of outside observers and transaction counterparties.
And about wallet fingerprints:
If different wallet apps connect to the same self-hosted Electrum server, the transactions they generate will have different wallet fingerprints?
if different wallet apps connect to the same Bitcore Core Node, will their wallet fingerprints also be different?
If the same wallet app connects to either a self-hosted Electrum server or a self-hosted Bitcore Core Node, will the wallet fingerprint be the same?