I'm pretty sure the (now) correct answer here is rfc7231 - section 7.1.1.1 It specifies Date/Time Formats and is where the HTTP-date semantics are defined.
HTTP-date    = IMF-fixdate / obs-date
Also we can see that
When a sender generates a header field that contains one or more
timestamps defined as HTTP-date, the sender MUST generate those
timestamps in the IMF-fixdate format.
So for a server sending a "modern time HTTP header"- where the value is a HTTP-date the format is equivalent to the IMF-fixdate format.
So to answer the actual question.
Which RFC describes the format used for date/time in the modern time
HTTP headers
You need to know the definition of  IMF-fixdate - which is in rfc7231.
It also give the definition of obs-date too i.e rfc850-date / asctime-date
     IMF-fixdate  = day-name "," SP date1 SP time-of-day SP GMT
     ; fixed length/zone/capitalization subset of the format
     ; see Section 3.3 of [RFC5322]
     day-name     = %x4D.6F.6E ; "Mon", case-sensitive
                  / %x54.75.65 ; "Tue", case-sensitive
                  / %x57.65.64 ; "Wed", case-sensitive
                  / %x54.68.75 ; "Thu", case-sensitive
                  / %x46.72.69 ; "Fri", case-sensitive
                  / %x53.61.74 ; "Sat", case-sensitive
                  / %x53.75.6E ; "Sun", case-sensitive
     date1        = day SP month SP year
                  ; e.g., 02 Jun 1982
     day          = 2DIGIT
     month        = %x4A.61.6E ; "Jan", case-sensitive
                  / %x46.65.62 ; "Feb", case-sensitive
                  / %x4D.61.72 ; "Mar", case-sensitive
                  / %x41.70.72 ; "Apr", case-sensitive
                  / %x4D.61.79 ; "May", case-sensitive
                  / %x4A.75.6E ; "Jun", case-sensitive
                  / %x4A.75.6C ; "Jul", case-sensitive
                  / %x41.75.67 ; "Aug", case-sensitive
                  / %x53.65.70 ; "Sep", case-sensitive
                  / %x4F.63.74 ; "Oct", case-sensitive
                  / %x4E.6F.76 ; "Nov", case-sensitive
                  / %x44.65.63 ; "Dec", case-sensitive
     year         = 4DIGIT
     GMT          = %x47.4D.54 ; "GMT", case-sensitive
     time-of-day  = hour ":" minute ":" second
                  ; 00:00:00 - 23:59:60 (leap second)
     hour         = 2DIGIT
     minute       = 2DIGIT
     second       = 2DIGIT
   Obsolete formats:
     obs-date     = rfc850-date / asctime-date
     rfc850-date  = day-name-l "," SP date2 SP time-of-day SP GMT
     date2        = day "-" month "-" 2DIGIT
                  ; e.g., 02-Jun-82
     day-name-l   = %x4D.6F.6E.64.61.79    ; "Monday", case-sensitive
            / %x54.75.65.73.64.61.79       ; "Tuesday", case-sensitive
            / %x57.65.64.6E.65.73.64.61.79 ; "Wednesday", case-sensitive
            / %x54.68.75.72.73.64.61.79    ; "Thursday", case-sensitive
            / %x46.72.69.64.61.79          ; "Friday", case-sensitive
            / %x53.61.74.75.72.64.61.79    ; "Saturday", case-sensitive
            / %x53.75.6E.64.61.79          ; "Sunday", case-sensitive
     asctime-date = day-name SP date3 SP time-of-day SP year
     date3        = month SP ( 2DIGIT / ( SP 1DIGIT ))
                  ; e.g., Jun  2