uuidgen 10k times and noticed that the 13th digit is always 4.
Why is that?
You can find a full explanation in the Wikipedia article on UUID.
UUID's come in different versions. The 4 you highlighted indicates version 4 was used where the UUID is created by generating a random number. Other versions use for example the date-time and MAC address of your computer.
When you look further at the first character of the next block you will see it is not very random either: it shows only the characters 8, 9, A and B . This is because the two most significant bits are
01 for the variant of this UUID version.
It's the version number of the UUID type /algorithm. This is a version 4 UUID which means that it's made using an upstream OS random number generator, rather than made from a namespace or network card MAC. It also means that it only has 122 bits of entropy, rather than the 128 you thought it did. That's still 5 undecillion values, but less than you thought.
See the wiki article for more details, especially the version types and other restrictions on the format.