IIRC, MIME (used both for Mail and for HTTP) allows to invent non-standard "experimental" headers by prefixing them with "X-".

Correct, though its use is now discouraged - from RFC7231 (emphasis mine):

Authors of specifications defining new fields are advised to keep the name as short as practical and not to prefix the name with "X-" unless the header field will never be used on the Internet. (The "X-" prefix idiom has been extensively misused in practice; it was intended to only be used as a mechanism for avoiding name collisions inside proprietary software or intranet processing, since the prefix would ensure that private names never collide with a newly registered Internet name; see [BCP178] for further information).

And the linked RFC6648 is dedicated to discussing the deprecation, with some interesting background in the appendicies.