Theres no such thing as your bitcoin tho, the only time when deposits to hot wallet get potentially connected to a cold wallet is if they were sent to a cold wallet and then spent again with some of the other utxos. Or when consolidation happens which occasionally does otherwise you havw way too many utxos in hot wallet which can be very cost inefficient in high fee env. There used to also be lots of dusting attacks that were meant to connect thinga together but that just meant that your tx consruction code needes to have a shitlist od utxos
