IIRC, it was the voice actress who does the computer voice who decided to say "D-7" for that scene having recently been doing Klingon research and knowing that's what the main Klingon ship from TOS was called, not realizing there were plans to use a different ship in that scene.Which I still believe was a script error/mistake/oversight and that design was not actually intended to be a D7, because they had names for all the Klingon ships behind the scenes, and that one was not called a D7.
I think the writer just threw the name into the script as a TOS reference without considering that they didn’t actually have a D7.
The F appears to be the biggest of the three, while the D is bigger than the E.So which bigger, the Enterprise F or Enterprise D or Enterprise E?