I find curious that mirror!Dukat didn't appear in the series, I dare to imagine that he would be more noble and celibate, lol, I went too far, sorry xd........is he?!
I tend to not go the “Opposite Day” approach with mirror universe personas because despite that common preconception, that’s not really how the actual episodes pan out. While some individuals are wildly different (Brunt, Worf, Bashir), others are clearly fundamentally the same person in certain crucial personality traits, tendencies, or beliefs (O’Brien, Jadzia, Quark, Rom, Tuvok, Garak) altered by different circumstances, sometimes greatly, leading to them being hardened, but still having a familiar spark deep in there somewhere (Sisko, Ezri, even Kira)
Thusly, I don’t think Mirror Dukat would necessarily be a good guy, he’d still be raised in a deeply fascist society, one arguably even more arrogant about itself than the prime Cardassian Union due to the Alliance’s victory over the Terran Empire. One where enslaving others is normalized and omnipresent, the occupation of Bajor in essence occurring across dozens of worlds.
If one wanted to do the hero route you can say he was exposed to so much cruelty it became overwhelming and he had to get away from it. The Alliance villains we get I have my own headcanons for how they turned out.
My theories are that Worf was raised to think that all of this was correct and the way things should be, simply indoctrinated. Garak was indoctrinated to, but he’s gotten a point where he feels trapped in this system and wants to move up in station to get out somehow. I’ve always seen Mirror Garak as a peak into how miserable Prime Garak would’ve actually ended up if he wasn’t exiled. Kira I think is reeling from trauma incurred during the Terran occupation of Bajor and acts in cruelty out of revenge, this trauma also manifesting in her need for control of her situation at all times and refusal to be vulnerable, even with people she loves like Sisko, Ezri or her prime counterpart (even when she wants to be)
Dukat likewise would likely have been indoctrinated as well, and as mentioned above something could’ve snapped him out of it, or he could’ve reveled in the Alliance’s fascism and become an embodiment of their ways. We sort of see the approach in the mirror universe novels, where he eventually becomes the head of state of the Cardassian half of the Alliance, “Supreme Legate Dukat”, without the Dominion needing to install him like in the prime universe, suggesting his political cunning might be greater than that of prime Dukat.
Thematically, as the Intendant is in some ways like prime Dukat, Mirror Dukat could share some attributes with prime Kira. Maybe he’s more loyal to the Cardassian state and more selfless, somewhat like Damar, but also with an independent streak for how things should be done, again like Kira, which leads to him potentially pursuing power for the above approach.
Regarding his sex life… I think his fetish for Bajorans could end up still manifesting, though he would be able to marry Tora Naprem publicly rather than with shame, except from the most purist of Cardassians. I prefer to imagine he simply doesn’t encounter Kira Meru at all in the mirror universe. Everything we see of the Intendant has me believing her parents likely died when she was young.
If the appeal is his own power and dominance in the situation, he could I guess end up developing a fetishistic view of Terrans or Vulcans instead. Not my favorite thing to think about.
The mirror universe has always had an element of humor to it, so honestly I don’t mind the celibate idea as just a funny reversal, both of prime Dukat and of the mirror universe itself, where characters are thought to be hornier (even if not by much in some cases)
Circling back to the Bajorans and the post I made headcanoning him as a political rival to Kira, if this Dukat is a true blue patriot of the Cardassian state, he wants Cardassia to be more powerful. In the aforementioned novels this manifests in chafing against the Klingon Empire’s relatively stronger position in the Alliance, and it could also manifest in him disliking the idea of allowing “weaker” peoples to become Alliance members and wanting to simply occupy and control Bajor rather than welcome them as allies. Maybe the Klingons are the ones who pushed for the Bajorans to join because they saw them as fellow warriors who had endured Terran oppression, since based on Discovery the mirror Klingons likely would’ve had to do a lot to reclaim their empire. The Cardassians could be less interested in this, particularly Dukat (he may be old enough to remember when Bajor was brought into the Alliance)
But the Intendant, for all her evil, still values Bajor’s independence as much as prime Kira, and pushes back, enforcing her planet’s boundaries
I think that’s enough of a ramble lol, I hope this was interesting