a computer powerful enough can guess all possibilities in a matter of minutes, and query them all against the db to discover all files stored within.

Again, it would be computationally infeasible on any reasonable timescale of human existence. It's no secret what every possible UUID would be, it's the fact there are 5316911983139663491615228241121378303 of them and trying each one would be futile. They're actually all on https://everyuuid.com/ to see for yourself.

Just for shits, I encrypted a file with a password being a UUIDv4. Here's the encrypted file as base64:

YLIR6fL46HfRmueb1tZWiQUFQHYnZOKO9oujOzhvWYpfTtB5RnHtAvMgUgeIsffLC1wz7D17Vp0VT5YIJMb5pA==

Here's everything you would need to do to decrypt this file with a password:

$ echo "YLIR6fL46HfRmueb1tZWiQUFQHYnZOKO9oujOzhvWYpfTtB5RnHtAvMgUgeIsffLC1wz7D17Vp0VT5YIJMb5pA==" | base64 -d > file.enc

$ openssl enc -aes-128-cbc -d -nosalt -in file.enc
enter AES-128-CBC decryption password:
u/01189998819991197253@infosec.pub can't brute force this

The password to decrypt the file is a UUIDv4. See if you can try every UUID and figure out which one I used as the password.

The powerful enough computer doesn't exist, and will not exist for some time. And even if it exists, it can't query the web server fast enough to have meaningful effectiveness.

So, for all intents and purposes, it's impossible. Period.

Aside from the fact that a strong enough supercomputer won't exist for decades, you're not limited by the speed of UUID generation. Even if you had an infinitely fast supercomputer, it wouldn't speed up your brute force attempts, since you're limited by the speed of the backend. Wherever Tea stores their images, that server has only a limited capacity for responding to requests, far less than the speed with which you can generate UUIDs. That's a hard cap - you won't try guesses faster than that.