The Deprecation HTTP response header field is used to signal to consumers of a resource (in the sense of [URI]) that the resource will be or has been deprecated. Additionally, the deprecation link relation can be used to link to a resource that provides additional information about planned or existing deprecation, and possibly ways in which clients can best manage deprecation.
I have no idea what are you talking about. Setting a request/response header is not bloating HTTP. That’s like claiming that setting a field in a response body is bloating JSON.
Proper HTTP implementations in proper languages utilize header-name enums for strict checking/matching, and for performance by e.g. skipping unnecessary string allocations, not keeping known strings around, …etc. Every standard header name will have to added as a variant to such enums, and its string representation as a constant/static.
Not sure how you thought that shares equivalency with random JSON field names.