I’m looking for activities or games for annie and i to play and bond over. she is always tapping at me to pay attention to her but when i get her out she is constantly flying back to her cage, but then starts call for me again. I have a nice java wood perch for her to play on, but she normally just sits and relaxes. i’ve had her for over a month and she steps up and comes out of her cage for the most part on command, but i’m looking on how to really bond with her in this specific situation

How old is she? Something my budgies really enjoy is clicker training. I've taught them all sorts of tricks and they love the active engagement and praise. A good youtube channel for this is called BirdTricks; here's one with their blue macaw Jinx
How I Train My Own Birds | How to Train a Parrot - YouTube

she is younger than a year, i believe she is only about 6 months old

She should be very eager to please then! Other than the clicker training, my two love peekaboo and trying to get a treat out of my hand (obviously this only works if your bebe isn't scared of hands). They also love it when I talk to them through a paper towel roll and make silly noises at them (especially farting noises lol) and will chase me around to try and stick their heads in the other end of the roll hahaha

she’s having a hard time focusing on me, and not trying to fly back to her cage despite me covering her cage with a blanket so she cannot see it. she flys off her tree every 2 minutes to try to get back to her cage

omg she just fell asleep next to me for the first time, isn’t that a good sign for taming?

Yes, that's good. The fact she fell asleep means she's comfortable next to you and beginning to trust you.

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You're doing fine considering that you've only had her a month. More importantly is to be patient and back off on trying to make her do something that she's not interested in doing ...for now. With positive reinforcement reward she may be convinced to participate, but birds don't always perform to your expectation. I'd just give her more time and gradually you should see her become more interested in "doing things" differently than she's used to. Good luck.

Please don't cover her cage. I know it's frustrating and you want to be besties right away but her cage is her 'safe space' where she can go to if she's really frightened, even of you. It sounds like your trust bond isn't the strongest at the moment, so what I suggest is starting from the beginning and going slow. Just sit next to her open cage and read to her or hang out near her (on your laptop, whatever) so she knows you are a safe good person at all times. Sing to her, talk to her, just be cheerful and calm near her. If she plays with a toy or checks out something you can say things like 'Oooo, that's interesting! What's that Annie?' in a cheerful voice. The main goal is to try and present yourself as safe, calm, and entertaining in a passive way. There's some stickies about it, I'm sure!

I missed the part where you indicate you are covering her cage where she can't see it.
Moira is correct - you should not be covering her cage,

Covering her cage is not helping her learn to trust you.
She should be allowed to return to her safe place whenever she feels the need to do so.
By depriving her of that option, you are trying to force her to behave as you want her to rather than allowing her to make the choice.
Please slow down and work at her pace.

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