If I create a new receive address in the hot wallet.dat and send the Bisq balance to it, is this identical privacy-wise as it would be for me to create a new wallet.dat and send the balance to it instead?
The privacy implications should be the same. By themselves, addresses don't tell you anything. It is the way you use those addresses that has privacy implications and that applies equally in the two cases you describe.
is there some sort of "extra tell" which reveals that I just sent the money back to my own wallet
Not in the way you mean.
Obviously if you, for example, later include some UTXO's from the new address with some UTXO's from an old address in a single transaction, observers may be able to make some inferences. There may be a higher probability of you unintentionally doing this if all the UTXOs are in one wallet.
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