I wonder if there is a way (e.g. a unique and stable ID), other than the full link, that one can use to cite a post, in the same vein as we can cite a journal article via its DOI.
As noticed in the comments, the shortest link is
https://stats.meta.stackexchange.com/q/6414 (this question), where the
questions/6414 part of the URL got shortened. It can be obtained from the "share" button, but it also appends your user ID creating something like
35989 is my user ID.
So if I want to cite, say, this post within another post X, will it work by using only the key '/q/6414' in the "link" field of post X?
If you want to use only the string "/q/6414" as a reference then I'm afraid it would be meaningful only to a small subset of users of this site that understand how its API works. It also does not mention which StackExchange (or other) site this part of the link refers to (maybe
https://stackoverflow.com/q/6414?). If the link needs to be useful as a reference, it needs to be meaningful for the reader.
If you need a shorter link, you can always use one of many URL-shortening services available online. For example. Bitly created
https://bit.ly/3yvSSCJ for the link to your question. There are some downsides to URL shorteners; this article lists some of them. https://www.geeksforgeeks.org/pros-and-cons-of-url-shorteners/