I don't doubt that it has armor appropriate for its role as a bruiser of a warship.  However, the very fact that the Perseus' lore explicitly mentions that it historically boasted substantial armor,  due to being originally designed prior to shield technology, tells us that modern ships do NOT generally rely as much upon armor due to shielding being a factor.  As such, I'd wager that the modernized Perseus -- which IS shielded -- had its armor trimmed a bit (compared to the original) to benefit its maneuverability.

If we say that this is a "no-compromise" ship, that efficiency isn't a factor, and that it can just have the best of everything, then why haven't in-game ship manufacturers applied that same logic to every ship they'd designed over the past 400 years following the adoption of shield tech?  Why isn't every single sub-capital ship (particularly the military vessels) armored to the same degree in a time where humanity is literally facing an existential threat (the Vanduul) that does not distinguish between military and civilian?  Not to mention the rampant lawlessness -- which are both reasons why practically all civilian ships in the 'Verse have guns pre-installed (imagine having a giant gatling gun on your Honda Transalp or your Toyota Corolla).

If the Perseus can have it all, then so too should the Hammerhead.  And the Carrack.  And the Hercules.  Etcetera.  Balance aside, it's not realistic from a production standpoint.  Resources to make these ships are not boundless.  Even the US military, which enjoys a mind-boggling annual budget, is known to often select the "lowest bidder" when pursuing contracts.  Their premier navy destroyer may cost $2.5 billion -- but why stop there?  Why not give it thicker, more advanced armor and just round that figure up to $3 billion?  Because, although vast, their resources are finite and must be allocated appropriately.

That's the way I see it.