We did....

New cat in a room for 2-3 days. That room happened to have a window, which was nice. We put one of old cats beds in there.

Then...

Old cat in a room for a couple of days while new cat explored the house. Left the old cat/new cat bed in there. Fed them on either side of the door. They started pawing under the door without hissing. That's when we opened it.

They became good buddies.

Now i have a third cat and it's a shitshow.

Yeah you really did not introduce them the right way. You should start over and do it properly, but first you should take him to the vet to get checked for contagious diseases that can be fatal to cats as you would not want to spread it to yours. They can also check for a microchip in case he is a lost pet.

After that, you need to set aside a room that is not important or favoured by your cat Anya, and designate that as his room. You should also give Anya a space where he is not allowed to go at all so she feels she has a safe space from the intruder. Here is some instructions how to do this properly, it may take weeks or longer for them both to be comfortable:

https://spca.bc.ca/faqs/how-introduce-new-cat-old-cat/

There are lots of similar instructions available. But you always start with them separate, then bring them something with the scent of the other one like a blanket (not pee or litterbox), then allow brief visual contact with a barrier, allow them to explore eachothers space when the other one is confined somewhere else, and then allow them to meet and interact while supervised, then allow them to interact unsupervised. Each stage can take anywhere from hours to weeks, but you cannot proceed to the next step until they are both completely comfortable. Cats are easily stressed at times and can stop eating or peeing and this can cause serious harm to their health or even be fatal.

You did it wrong. Anya's world is upside down with this intruder. "Just see what happens" is not healthy or safe. Accept that and move past it.

As another comment mentions, Jackson Galaxy has a good many videos on this topic, but the first priority should be the vet to check them out for a chip and health. Then watch the JG vids.

Remember: cat's most important security is derived from familiar territory. Move even one piece of furniture and they need to reassess. A new un-neutered male is a direct threat to the territory and can cause many unwanted behaviors and stress on both cats.

I foster and have 2 resident cats, so I do introductions a few times per year. I highly recommend Jackson Galaxy's guide. I've linked part 1, but there's 5 parts, the rest are linked within. It's worth reading the entire thing, because he does a great job of explaining why he recommends each step, which is helpful if you need to modify things a bit.

You need to figure out a room in your house that can be The Boy's basecamp. This is where The Boy is going to spend most of his time until Anya can tolerate him, and hopefully isn't a "high value" space for Anya. Without knowing either cat, I'd say you should plan for a minimum of 2 weeks of very carefully managing the process of introducing them to each other, and probably at least a month before things really settle in.

Also, make sure The Boy gets neutered ASAP, if he isn't already!

When I adopted Siefrieda, the way that I introduced her and Kika (my older cat; she's now 16, I think she was 10 back then) was like this:

• let Frieda in the carrier box. In the living room, so Kika could smell it.
• let cats each in one part of the house, split by simply closing the doors. In my case it was laudry room + patio vs. the rest of the house.
• switch the cats twice~thrice a day. That lets them get used to each other's smell, plus it gives them access to both sides of the house. Typically when I went to sleep Kika would have the main part of the house, as unlike Frieda she was already used to her home.
• put their food on both sides of a glass door. At first they avoided eating at the same time, but when they were OK with it I knew that they didn't mind too much each other.
• open a slid on the glass door, not enough for a cat to pass, but enough for a paw. Let them smell each other "on the live". When Kika was mildly curious with Frieda instead of aggressive, I knew that I could let them in the same room and they wouldn't fight.

Nowadays they aren't best friends, but let's say that Kika tolerates Siegfrieda like you'd tolerate a really annoying kid. The only main issue is that only one of them refuses to share a litterbox, but I'm fixing this.

I had two males where one had been established and they didn’t become buds until we moved to a new place and both were on neutral ground. It’s not very practical, but it worked like a charm. That’s not why we moved. Just a nice side effect.

Glad to hear things have settled down a bit! Feel free to ping me or PM me if you need to bounce any plans off a real person, particularly when it comes to modifying things to work with your situation and/or gauge when to move on to the next steps. I'll be keeping an eye out for your updates either way.