Let's go a step further and just iterate through them on the client. I plan on having this phone well past the heat death of the universe, so this is guaranteed to finish on my hardware.

  function* uuidIterator() {
   const bytes = new Uint8Array(16); 
   while (true) {
     yield formatUUID(bytes);

     let carry = 1;
     for (let i = 15; i >= 0 && carry; i--) {
       const sum = bytes[i] + carry;
       bytes[i] = sum & 0xff;
       carry = sum > 0xff ? 1 : 0;
     }
 
     if (carry) return;
   }
 }
 
 function formatUUID(b) {
   const hex = [...b].map(x => x.toString(16).padStart(2, "0"));
   return (
     hex.slice(0, 4).join("") + "-" +
     hex.slice(4, 6).join("") + "-" +
     hex.slice(6, 8).join("") + "-" +
     hex.slice(8, 10).join("") + "-" +
     hex.slice(10, 16).join("")
   );
 }

Once you deliver that, you can also think about a database of natural numbers!

https://everyuuid.com/

Kolmogorov said that computers do not help with naturally hard tasks; they raise a limit compared to what we can fo manually, but above that limit the task stays as hard is it was.

I think there's a subset of people that offload memory to their browsers and that's kinda scary given how these fingerprint things work.