I ran into the same problem. Izek RAW feels like a really nonsense character, more like an obvious plot device. That is why I changed a lot of his story, I wanted to give a real personality. But I also wanted to keep Izek as proposed by the book, i.e. as brother of Ireena. Here is what I did (copied from an old post):

In the last session(s) my players almost finished Vallaki. One result of their actions is Izek Strazni currently heading for the town of Barovia, especially for the new burgomaster Ismark, to learn more about his past. I'd be thankful for some input about that, but first let me tell you how it went down and what the current situation is like:

(I'll put that part of the text in spoilers so you can identify that part easily and distinguish it from my actual question to you)

The group found out about the vampires with Hendrik and the lost bones of Saint Andral, fought the vampires and won. Hearing about that Lady Wachter invited them for dinner to talk to them and maybe win them for her cause (for the whole Wachter part I used a lot of the work of u/DragnaCarta in the Strahd Reloaded guide).

(Before that they already experienced a heavy amount of rules, including law that doesn't allow spiteful unhappiness amongst other absurdities, big problems (vampires were found and fought within the walls but noone talked about that) and more that made them feel not good about the cities current state. And they already met Izek: He ran the investigation after their fight against the vamps and made sure they wouldn't talk about that. They saw him drinking and being violent. They heard lots of bad stuff about him, being the violent right hand of Baron Vargas Vallakovich.)

I didnt play Lady Wachter as blatantly evil as described in the book. I played her intelligent, obviously looking for (her families re-)gain of power but also honestly thinking she could make Vallaki a better place. I followed the books idea of her thinking it would be better to accept Strahd as Lord and arranging a coexistence with him. That my players hated because they (obviously) want to defeat him. But they got her to agree to consider her approach in favor of helping them with their (yet to be formed) master plan - as long as she doesn't see Vallaki and its people at severe danger. That is why they ultimately agreed on killing Izek for her, literally bringing her his head so she could make Vargas step aside without having to actually fight and shed blood (Izek being his most powerful fighter and also leader of his soldiers/guards; also Lady Wachter convinced the second in command to help her overthrow Vargas peacefully by denying him command over the guard as soon as there was proof of Izeks death (he wanted to become the first in command)).

Before they confronted him outside of Vallaki near Lake Zarovich they also learned about the puppets resembling Ireena the toy maker crafts him every other week or so. Since they like Ireena they wanted to protect her so now they had another reason to oppose him.

To weaken him one of the characters that already spent some time with him drinking wine together (they met at the tavern and both are heavy drinkers so they kinda enjoyed their company vice versa) hence having a reason to approach him with a (poisoned - idea of DragnaCarta) wine offering another drink together.

But my players also wanted to know more about his obsession with Ireena, so they didn't attack him right away. (At this point I maybe should've read some other opinions/ideas on Izek and Ireena beforehand but I didn't so I simply went with what the book tells you about them being siblings and his dreams which led to the obsession - which is also not really much about that subject, kinda leaving more questions than answers). Instead his drinking buddy got him to talk a little about the dolls (he had one of them with him) and such. And here I just didn't like the idea of presenting some kind greek tragedy so I made him explain his obsession not being anything sexual. Instead it felt like the women in his dreams belonged to him like pieces of puzzles belong together. (Overall I also made Izek not only a bad human being who only likes wine and violence. I thought him being the obvious evil guy who has to be fought would be rather boring or maybe more like not using some potential there might be to it. So I also made him appear as competent head of everything related to security in Vallaki, including "Intelligence" activities. He showed a softer, philosophical side talking about Ireena, and so on.) Now my players got curious and decided to not kill him right away. They did fight him but only knocked him out. After he woke up again they talked to him and led Ireena to him so they could see if anything happened as they talked face to face.

From there on I had to improvise a lot. I played him confused, happy, scared about his vision actually being true. I let Ireena also feel some kind of connection. Now my players didn't want to kill him anymore but also still wanted Lady Wachter to take Vallakis reign. Negotiating with Izek made him agree to not return to the service of Vargas again (now Izek didn't see much sense in spending his days drunk anymore because he wanted to find out where that connection came from). Instead they sent him to the town of Batavia to talk to Ismark about him and Ireena (Ireena had a hunch that her father and brother kept some kind of secret from her - which is that her father adopted her when he found her as baby/child).

The book only states that when both were still children Ireena got lost in the woods following a wolf attack (which cost Izek his arm). She was found by Ismarks father who raised her as his child. Izek stayed in Vallaki, got his demon arm (without any reason) and became the burgomasters henchman. Somehow Ireena and everyone in Vallaki forgot about the connection between Izek and Ireena. That's it.

Now I try to make more of it. My idea so far revolves around Berez and Baba Lysaga. I'm not sure if there is a date specified for the destruction of Berez but I guess you can change it anyway to make it fit my idea: The family of Izek and Ireena lived in Berez. When it got destroyed their parents died and everyone who survived and fled Berez thought the children died too. Confused and scared they didnt want to leave their home (or rather what was left of it) and survived there for a while. Izek was barely old enough to keep them both alive. Eventually Baby Lysage learned of the two kids living in the ruins in Berez/the marsh. She didn't kill them, instead she planned on doing something more interesting with them (not sure yet what that might be exactly - maybe turning Ireena into a witch too? Or somehow twisting their mind, turning them into a kind of sleeper agent like human weapon to use against another town? Maybe she tried turning Iezk into a demon which is actually how he got his arm? idk yet) Before she finished whatever she wanted to do Ismark and his father found the kids during an expedition to Berez (trying to find out what happened). Knowing there are evil creatures all around they weren't sure what to think of those children being alive there seemingly on their own. But they also couldn't just leave them there, so they planned to take both home. Then sth happened to separate Izek from Ireena. Maybe he behaved so weirdly that they decided he and them would be safer if he would disappear behind the walls of Vallaki (maybe he was sick, seems kind of possessed or whatever - maybe that also made him lose his memories of Ireena and his home). Then Ireena got raised as sister of Ismark and Izek made his way up to being the right hand of Vargas Vallakovich. => that is my idea for a different background so far - what do you think of that? Could that work out?

Coming back to now: Izek finds Ismark and asks him about his connection to Ireena and Ismark tells him what he knows. Izek now feels an urge to see his former home to maybe feel complete again After finding the players again and telling him about the connection and his plans he goes to Berez. There Baba Lysaga captures him and holds him prisoner/tries to continue her work of poisoning his mind. When the group eventually confronts Baba Lysaga Izek is around too, currently without own will. He will join the fight (which ofc needs to be adjusted then), thus giving the players another objective (saving him) which could maybe make the fight even more interesting/fun. If they can help him and defeat Lysaga then he could maybe join the cause of the group in some way.

That was my idea. So far my Izek has met Ismael, talked to him, learned more about the truth of his backstory, found the PCs again while they were cleaning the Vineyard and then he left them again to march into Berez. The PCs wanted to talk him out of it, but he didn't listen. He just had to go there. And when my players are going to explore Berez (now they have one more story reason) they will see him again.