Is there a way to run an entropy check on my cold card seed + passphrase using the cold card device? While keeping it offline, of course?

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no. but it would be possible to have a script checking resultant xpub against a table of those that would be derived from weak entropy (e.g. only a few dice, few words, common phrases).

The dataset would be too large to fit on a coldcard, but could conceivably be loaded on a disconnected laptop running tails

You could just use tails with the keepass that's on it. Then type your seed phrase in the password\passphrase generator and keepass will give you an approximate calculation of entropy.

You're welcome..🤔😊