Thanks for the clarification.
question remains whether the unusual exterior features (i.e. apparent saucer module separation capability, matter-antimatter-reactors in the front caps of the warp nacelles, disproportionate size of secondary hull in comparison to saucer hull etc.) are sufficient evidence for a pre-TOS design lineage.
Regarding the interpretation of the three-digit registry I think it depends whether you prefer that just three-digits indicate classification and/or type or the vessel or
the first digit which in the case of "638" would indicate a "cruiser of the 6th Federation design", according to Matt Jefferies, the father of the Enterprise.
Where it gets a little confusing is the distinction between "cruiser" and "starship".
His original TOS pre-production sketch with the "cruiser" reference could come from the pre-production stage were the Enterprise
was just a cruiser before that changed to "Starship" (as a type she would become "Space Cruiser").
Considering that already the pre-TOS Archon
was a "starship" according to Kirk (please not another history "lesson"...
), I assume Jefferies would have revised his "cruiser design" to "starship design".
Alternately, one may assume that the design series from # 1 thru #17 featured equally cruisers or starships.
But there must be a distinction between "cruiser" and "starship" according to Scotty in TNG's "Relics": "I served on a freighter, a cruiser, and a starship."
(unless and in retrospect the Enterprise
was that cruiser and the Excelsior