I think somebody chose very unfortunate name for STATELESS concept and that's why the whole misunderstanding is caused. It's not about storing any kind of resources, but rather about the relationship between the client and the server.
Client: I'm keeping all the resources on my side and send you the "list" of all the important items which need to processed. Do your job.
Server: All right.. let me take the responsibility on filtering what's important to give you the proper response.
Which means that the server is the "slave" of the client and has to forget about his "master" after each request. Actually, STATELESS refers only to the state of the server.
https://www.ics.uci.edu/~fielding/pubs/dissertation/rest_arch_style.htm#sec_5_1_3