The UUID standard has several versions. Version 4 for example is based on a completely random input. But it still encodes the version information and only uses 125bits of the possible 128 bits.
But for transferring these via HTTP, it is more efficient to encode them in BASE64. There are libraries for this (https://github.com/skorokithakis/shortuuid).
But what I am wondering: Is there an alternative standard for shorter ID-strings? Of course I could slap together a version-byte + n random bytes and encode them BASE64, having my own working 'short, random ID scheme', but I wonder if there is any alternative that someone already specified before I make my own.
There is no standard for anything shorter.
Numerous folks have asked the same question and all come to the same conclusion: UUIDs are overkill for their specific requirements. And they developed their own alternatives, which essentially boil down to a random string of some length (based on the expected size of their dataset) in a more efficient encoding like base64. Many of them have published libraries for working with these strings. However, all of them suffer from the same two problems:
If neither of these problems affect you, then feel free to pick any of the various schemes available or roll your own. But do consider the future costs if you discover you're wrong about your requirements and whether the cost of having to change justifies whatever minuscule advantage in space or complexity you get by not using a proven, universal system from the start.