The answer
Cold storage keeps signing keys offline, but it does not hide Bitcoin transactions from the public blockchain. Address reuse and UTXO merging can reveal links.
What to do next
Use fresh receiving addresses and consider coin-control practices. Distinguish wallet-security protections from transaction-privacy protections.
Sparrow Wallet
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BitBox Bitcoin hardware wallet
A Bitcoin self-custody device to compare; it does not make on-chain transactions anonymous or prevent address linking.
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Frequently asked questions
Does a hardware wallet hide transaction amounts automatically?
No. Ordinary Bitcoin transaction amounts are visible on-chain.