She's just excited, budgies love to vocalize when they are excited and just having a good time. Additionally, she could be flock calling. You can try and encourage her to tweet and not squawk by only going up to her cage when she's tweeting, so at least over time she won't squawk to get attention. However, that's just about all you can do, as budgies love to express themselves vocally and a happy budgie is a loud budgie.
As a bird owner, its just something you're going to have to deal with. If the fiancÚ doesn't like it, he's either going to have to get used to it or move out
As for the apartment complex complaints, it's reasonable that your neighbours don't want to be listening to a screaming bird all day. Realistically speaking, the only two options are to rehome Annie or to move
I know that all sounds very blunt
But in truth, that's all you can do. She's a happy, healthy girl with everything she needs so she's going to keep chirping and squawking as she pleases.
Make sure to give her plenty of supervised out of cage time per day so she gets some of her energy out, and that she has a big enough cage with lots of toys, etc. Other than that, there's not much else you can do!
Best of luck with Annie! I hope things work out