It does remove a lot of entropy. The number of distinct bridge deals is 5 x 10^28 (source https://jlmartin.ku.edu/~jlmartin/bridge/basics.pdf ). log2 of that is under 96 bits, which does seem small by today's standards of cryptography.

As an aside modern bridge dealing machines/algorithms generate a 96 bit random number and do a one-to-one map to a particular deal (ie not doing lots of random calls and moving cards with a Fisher Yates shuffle, say).

Correct. This is to solve a different problem associated with Solitaire - keeping our keys in sync.

With Solitaire, if I miss a message that you sent, my decipher deck is now out of sync until we resynchronize somehow.

With bridge columns as the approach, each day the message has a different key that is kept in sync through the bridge columns. Missing a message doesn't result in desync.

Yes, this has low entropy compared to a shuffled deck of cards... and if someone can find out what the system used to generate the key is, it's all decrypted (I'm sure that various Three Letter Agencies are saving every bridge column that's been written).

This solves a problem that two people (or more! because that gets complicated too) may have in using Solitaire. If I were to use Solitaire with this means of key exchange, this would be something that would be low importance and temporal in nature where it doesn't matter if it is decrypted next week.

For example, during WWII Four Square was used ( https://en.wikipedia.org/wiki/Four-square_cipher ) and remains part of basic cryptanalysis in the US Military - https://archive.org/details/Fm3440.2BasicCryptAnalysis - even though stronger cryptography was available. It was usable by in the field to send encoded messages that needed to be sent now (without lengthy encrypt / decrypt processes) for information that had little to no value in the future.