Well, not really.
The designations represent a silly hodgepodge of systems. The Galaxy and Sovereign are lazily designated "class starship", which is inconsistent with the Defiant being "battleship". The TOS Romulan vessel from "Balance of Terror" is lacking a national identifier (and is given the designation Bird of Prey which certainly is not canon), yet the corresponding TNG villain vessel is called "Romulan Warbird". The Cardassian or Klingon military transport vessel silhouette (the graphic seems to be malfunctioning, we only see part of the Cardassian color scheme there) is called "military freighter", even though militaries only have transports, not freighters.
I'll give you Romulan Bird of Prey, but the rest of that is thin. The Romulan Warbird is what that ship is called. Yes, it has a class name, but that's still a Warbird. The idea that "militaries" only have "transports" is trying to force "Real world" terms into Star Trek. Canon doesn't work that way. To paraphrase a great thinker, it rejects your reality and substitutes its own.
Not really. Sisko simply says she is a warship. Nothing about "only" there.
Starfleet does not build warships. That's dialog canon. Yet Defiant is a warship, and Sisko spends time explaining the circumlocutions Starfleet went through to classify the ship. Given the competing concepts, that a warship exists, and that Starfleet doesn't do warships, it isn't a reach to say that Defiant is Starfleet's only warship class. Beyond that, canon designates no other Starfleet ships as warships.
I see no evidence that the E-E would have altered the situation in any way. If the Defiant outpowers the Galaxy, why should she not outpower the Sovereign as well? The E-E was never said to be particularly powerful - merely "the most advanced" in ST:FC, and that's a title that any number of ships can hold simultaneously, depending on which fields of advancement one wants to boast on.
Whether the Defiant really outpowers a Galaxy is another matter The statement above might be just
1) a truncation of "the most powerful ship for her size in the quadrant",
2) an indication that the ship's unique abilities give her great operational powers despite her carrying weak armaments and weak shields in comparison with proper large warships,
3) an indication that there weren't too many warships in that particular quadrant of the Bajoran Sector, or
4) a flat out lie to impress Riker.
Canon is canon. Speculation is speculation. Most of this is speculation. If the "most powerful ship in quadrant" line was a truncation, you need to provide evidence to support it. After all, I could reject your characterization of the statement refering to a sector, and point out the word was "quadrant." So, the most powerful ship in the Alpha quadrant. THAT would be pure speculation.
I don't claim that the Enterprise E is more powerful than Defiant. I simply allow that the designers tend to lean on fan expectations. Fans expect the Enterprise to be the newest, biggest, fastest, bestest. The production may be simply implying these features, or it may intend them. That is, as far as I'm aware, unknown. As far as I'm aware. Allowing the E-E as "better" than Defiant was simply a way of disposing of that potential objection.
Full Disclosure: The exact line is "one of the most heavily armed ships in this quadrant," and is delivered by Dukat to Sisko, so it definitely wasn't a means of sucking up to Riker. The main reason for noting that line was to point out that Cary's logic for claiming the Defiant was not a battleship was flawed. As one of the most heavily armed ships in the quadrant, Defiant meets one of the definitions of "battleship."
Pure speculation. And as far as we can tell, "escort" is a pure warship, because escorting is a pure wartime mission without any civilian tint to it.
It's bad form to engage in a behavior and then turn around a chide the opposition for the same thing. Smacks of politician's think. Fortunately, I didn't do any "pure speculation," there.
Starfleet is a semi-military organization. I don't see anything civilian about the canon designation "heavy cruiser." Again, you are injecting "real world" logic into Star Trek. We don't know the complete classification scheme for the Starfleet. So the tint of a term is irrelevant. An Escort can easily be a purely defensive ship, and thus "not a warship." While this runs into the realm of speculation, it is speculation supported by the canon assertion that Starfleet does not build warships.
Escorting is not a purely wartime mission. You assume the only kind of raiding that ever happens is commerce raiding conducted by a government during a war. Ever heard of piracy? There are pirates in Trek canon. Piracy suppression can be, and is, a peace time mission. The United States is not at war with Somalia, yet is engaged--right now--in suppression ops against Somali pirates.
So while it is speculation, it is not "pure." It is a combination of known facts.
How so? Starfleet explicitly has an institutional structure in place that features numerous warship classifications, including dreadnought, cruiser, destroyer, frigate and escort - that's all in the dialogue. We haven't heard of a Starfleet battleship so far in dialogue, but we have heard our Starfleet heroes give the designation to enemy spacecraft, to wit, huge Jem'Hadar things that outclass anything Starfleet has ever fielded and perhaps indicate that Starfleet just hasn't gotten around to building any battleships yet.
The Central Intelligence Agency classifies operatives employed by foreign powers as "spies." But it calls it's own "agents" or "field officers." Spies don't like to be called spies. It sounds dirty. They don't mind using dirty words on their enemies.
Starfleet can easily call a threat vessel a battleship if that is what it is. If they wanted to, they could also classify it as duck. What they call enemy ships is not indicative of what they call their own.
At what point, and where, has Starfleet called any of its own ships "destroyers, battleships, etc?" The only case where this comes close to happening is the mention of fighters during the dominion war. I'll leave it as an issue for the reader to decide if a fighter is ship. (IMO, it isn't.)
That's just my opinion, but it still canon that Starfleet doesn't build warships. Dialogue, and the distinct lack of any Starfleet references to Federation warships aside from Defiant.
Why should we think that this is true? Because Kira jokes about it in a tense moment?
Why should we take Kira's statement to be joke?
Naah. The Constitution and Ambassador are. The other two are unknown.
Did you
read that link? Soft canon is still canon until it is contradicted by hard canon. The DS9:TM is soft canon. Sternbach's statements are soft canon. They stand until hard canon contradicts them. Given the current direction of franchise, it seems unlikely that that is gonna happen.
I don't like playing rules lawyer with canon. It is, ultimately, a fool's game. Canon contradicts itself, often and viciously. But there's been no definitive canon worthy statements of Federation destroyers, battle cruisers, battleships, dreadnoughts, monitors, stay-puft-marshmellowmen, or MOABs. And if we one day learn that Mr. Stay-Puft is the lynch pin of Sector 001's defenses, I'll have to eat my hat. But until that day, I'm going to stand behind the "no warship" theory because anything else is just an attempt to shoe horn wet-navy logic into Trek at the expense of one of the core ideals of the franchise--that the United Federation of Planets, and humanity by extension, has grown beyond that whole war business.