A search stated that there are 2048 seeds in the library.
You are making it too complex. A 12 word mnemonic is representing 128 bits of entropy. The chance of finding the same entropy is 1 in 2
128. And a 24 word mnemonic represents 256 bits of entropy...
I suspect that after some number of tries each cold wallet will do something like:
There are no such mechanisms in wallets not to mention that you could always write a script that searches the space on its own without needing the overhead of a wallet software. It goes without saying that it is a pointless code to write.