I don’t wanna sound rude but, are we reading the same thing?
First, a tyrant is a cruel ruler, a dictator, not a psychopath/sociopath, and if I remember correctly, ml did start a war to reunite the whole continent
Second, since the two met each other, the ml already admit that the mc was his type, not only that but like u said, he’s a man child with an attitude so he doesn’t get along with just anybody, yet they were very compatible at work and he admit that she did great in the last 5 yrs of work, so basically, she’s his type and they worked together for 5yrs and she managed to improve his temper, I’d say that’s enough for him to fall in love with her
Last, I’d like to remind you how quick to killing he was/is, when he first met the mc he was gonna kill her cuz she’s too much his type he thought it was a plot by his step mom, then he almost killed the mc of the original novel just cuz she was messing with the mc, he gets really mad whenever she’s hurt or cries and still has a terrible temper, he’s not what you’re looking for that’s for sure but he’s not a sane calm coward ml either

My pet peeve with this genre is when they say tyrant and cannot fully commit to it. They say the ml is the worst tyrant out there but he is just some narcissistic man-child with an attitude. Then he is saved by love of fl (who by the way does nothing interesting for the ml to fall that deep anyway).
When I hear tyrant I want batshit crazy, give me the jocker or Sangwoo (killing stalking) type tyrants who doesn’t falter for fl on first sight. Make me genuinely concerned for the fls life when she is near him and how she manages to come out alive each time.
Your weak ass pretty boys who are just tsunderes at most are boring. Sign of weak writing tbh. It's like the author doesn’t have enough capability to write complex character like that and make the readers not hate him. If you say tyrant, give me one you cowards.