The documentation in https://docs.python.org/3.8/library/http.cookiejar.html#http.cookiejar.CookieJar
claims the following for functions add_cookie_header and extract_cookies.

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The request object (usually a urllib.request.Request instance) must support the methods get_full_url(), get_host(), get_type(), unverifiable(), has_header(), get_header(), header_items(), add_unredirected_header() and origin_req_host attribute as documented by urllib.request.
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When reading the documentation for Request Objects https://docs.python.org/3.8/library/urllib.request.html?highlight=requests#request-objects
there is this:
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Changed in version 3.4: The request methods add_data, has_data, get_data, get_type, get_host, get_selector, get_origin_req_host and is_unverifiable that were deprecated since 3.3 have been removed.
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So basically the documentation claims that if the request object does not support functions that are removed then the headers will not be added. The code itself seem to do the correct thing however and add the header.