Suppose that (and this is not that wild a hypothetical under the circumstances) First Republic had been contemplating, barring significant new deposits, selling to an up-and-coming midsized bank, and the larger banks did not collectively desire that outcome.

Their CEOs can’t sit around a table and discuss joint billion-dollar strategic action. It’s the definition of a “conspiracy in constraint of trade”.

What constraint of trade results from this action?

If appetite for deposits is satisfied by some ingroup then the bank doesn't have to compete for deposits on the open market.

This would be an acquisition intention that's not been announced or registered already? Anything's possible, but it seems silly to worry about things like that.