Get yourself a copy of I, Strahd (read it or listen to it on audio book). If your struggling with Strahd’s perspective, that book will help.
Roleplaying Strahd
Despite what we already know about Strahd from the module book, there a mess of “character” that gets left behind in the older edition adventures and it doesn’t really follow Strahd into the current 5e adventure. This is partly because of how WoTC/the module writers chose to reintroduce the adventure to the current edition. We got some cool new things, but we lost some stuff too.
Strahd is a count/king that has technically been alive for around 1000+ years, although he’s been stuck repeating essentially the same series of events every few generations (when he closes his borders and begins searching for Tatyana’s current incarnation); this is stuff you won’t get from the module. Several hundred years passed between 3.5 & 5th edition, it’s silly to think that Strahd isn’t capable of growth in all that time; especially when we consider that Strahd has been around since 2e.
Strahd is old, he’s seen nearly everything that would considered “new” to most other worldly people. He expects to be treated with nobility by his subjects, he expects to be feared by his enemies/food, he expects to be loathed by adventurers because he deliberately brings them into his realm.
To Strahd, this is all a game. He’s played it before; and he’s tired of losing. So This time, the gloves are already half-off. Strahd doesn’t act like a child in the sense that he whines; but rather he deflects in a manipulative and commanding manner.
Nothing is Strahd’s fault, because the players actions made him do whatever terrible things he’s done thus far. Strahd “deserves” Tatyana’s soul, it belongs to him as it rightfully should.
Strahd knows that Tatyana cannot technically escape him, so he plays the long game. A creature of absolutely vanity; Strahd’s overconfidence is his ultimate weakness.
Strahd is the hero of his own story because he is an unjustly tortured man whom was tricked into making a pact with an ancient evil in the hopes that he could claim the love of person he most desired. Admittedly Strahd hates himself for what he did to Sergei, but he’ll never admit that to anyone.
Strahd is a paradoxical character because while he is arguably evil incarnate, he behaves as a benevolent individual.. right up until someone actually steps on his toes. Strahd will be nice to the players, to spite them, and in the same encounter; he’ll kill the cleric and then blame it on the party members.
“Your arrogance caused this, what kind of people come to foreign land and refuse homage to its king? Vagabonds and criminals.. that’s who. Never forget I gave you the chance to kneel, and I make you crawl.”
That’s what immediate popped into my head after reading your post; I’m sure other DMs that will have good advice on this. I’d also suggest looking at DagnaCarta’s and MandyMods adventure changes (on this Reddit), they both have great resources for playing Strahd’s manipulative nature to the max.
Take what you will, Ignore the rest. Happy DMing!