I was writing a reply at the same time as you, so time for a total rewrite.
What sort of ship is FR_Diligente? (An Essex equivalent is certainly unsuitable. Last time I ran into one of those, she had 18 pounder guns, so although not as impressive as an Artemise, it still falls into the category of "not the usual definition of 'smaller'".

)
Natividad is a 50 gun frigate, so approximately equivalent to an Endymion.
Lydia is a 36 gun frigate and is supposed to be inferior to
Natividad, so it can't be an Endymion. Moreover, Hornblower gets the
Lydia at the promotion to Senior Post Captain. "Nk.c" makes a special exception for Hornblower, who gets
Indefatigable while regular Post Captains get an Endymion (Revolutions era) or Steam Frigate (Napoleonic Era).
Indefatigable is a Razee, which seems about right for the
Lydia. That leaves the Unité as suitable for the
Atropos, which Hornblower should be getting after he's been married to Maria, not right after he leaves the house after proposing to her.

And that in turn leaves him in command of
Hotspur at the current end of the storyline, which can be a 6th rate frigate.
Incidentally, "Nk.c" makes no distinction between Junior Post Captain, Senior Post Captain and Captain. If we do, we can drop Midshipman and Junior Lieutenant off the bottom of the rank table, so that a regular naval character starts as Lieutenant, a more suitable rank to command even a little sloop.