The problem, Hans, is that the UK altered the medieval terms, where Knights were considered to be of the lowest rungs of the nobility, and has redefined them successively over time.
As for Imperial knights being Nobles, see: MT PH p10, p22, p27; MT IE p8, p14; CT S11, p34, 35; CT S04 p8
p10: "Those with Social Standing B + (11 or greater) are considered to be noble, and may assume their family’s hereditary title. Noble titles are commonly used, even if the individual is not engaged in local government. At the discretion of the referee, the noble may have some ancestral lands or fiefs on his or her homeworld."
p22: (Ranks of noble careers and notes on table)
p27: "Social Standing (SOC): A character’s social class. Standing 11 + holds a patent of nobility from the Third Imperium or similar interstellar governments. The individual is considered noble."
MT IE p8: "There is only one legitimate means to ascend to the iridium throne: by confirmation of the Moot, that governing body composed of all nobles (baron and above) of the Imperium." Emphasis mine. Note that Knights and Baronets are nobles by definitions in the PM, but are not "Nobles of the Imperium" but are nobles of a given domain.
MT IE, p14: "NOBLE RANKS
The lowest noble rank is knight; the highest is emperor (although the emperor and his family are not members of the Moot and in fact are prohibited from entering the Moot Spire on Capital unless invited by the body)." Emphasis original.
Ibid.:
"Knight: The lowest of noble ranks is knight, which is awarded
by the emperor or an archduke as an honorific rank in recognition
of achievement or service: as such, a knighthood is coveted
by nonnobles and is seen as more attainable than membership
in the peerage." Emphasis original.
Ibid: "Knights are not members of the peerage and are thus not
subject to all protocols. Knights instead belong to orders of
knighthood and are awarded privileges according to the order."
Clearly, MT IE and MT PM uniformly use Knights as Nobles, but Peers only for barons and above, and strongly implies by the Emperor's list citation that knights and Baronets are not "imperial" nobles but members of the domain orders.
CT S11, p34: The nobility includes within it a subset called the peerage, consisting of all nobles except knights and baronets. Except in extraordinary situations, to hold a high office in the lmperial bureaucracy, a person must be a peer (although not all peers hold office). This addresses multiple of your erroneous assertions, Hans...
1) it is clear that CT fluff also makes Knights nobles in the Imperium, and,
2) That high offices in the bureaucracy require peerages, not just the Grand Admirals
S11 p35: "NOBLE RANKS
"The lowest noble rank is knight; the highest level is archduke. (Above the archdukes is the special station accorded members of the lmperial family, but they are not considered part of the nobility.)" Emphasis Original. Note that this makes a royals distinction, but not by that term.
CT S04, p8: "The noble career is open only (and automatically) to persons with Social 10+. Rank corresponds to noble rank (taken from Social Standing) once position is achieved." Note that rank B is Knight, on the table immediately below the quoted paragraph.
CT agrees with MT. Knights are nobles, but not peers, and not "imperial nobles" but are nobles. Their nobility is a function of the Archdukal authority (explicit) and since they are explicitly also nobles, and explicitly not "Imperial Nobles", Imperial Nobles is a function of being a Peer, a vassal of the Emperor, rather than a vassal of an Archduke (even if that archduke is ALSO the emperor).