This is how my intuition went: it's probably less than 128
bits because UUIDs are 128 bits, and they're universally
unique.
But what's in a name? There's no natural law constraining the UUID standard, such that they must be actually universally unique. And 128 bits isn't such an incredible bit space.MD5 hashes are 128 bits, and prone to manipulating in favor of collisions.
Don't get me wrong, 3.402823669209385*10^38 is a huge number, and we haven't used enough passwords to occupy every value in that key space, but I still don't imagine 128 bits provides truly universally unique coverage, but really just pretty okay uniqueness coverage.