Oops. I acquired 6 English budgies over a year ago and it took them months for a few of them to come out on their own. They weren't afraid I don't believe. I think they were just content and lazy, not nearly as active as my regular budgies. I began leaving the cage door open all day long, only when we were home at first, and after a few months we left it open except at night. The room is our main living area and it's as bird safe as practical. They began coming out and sitting on top of the cage and making a few flights around the room. They now come out on their own soon after the door is opened in the am but go in and out all day and usually go in by themselves at night.
It helped that I had a couple regular budgies that came out much more readily. I assume she's your only bird so there's no bolder bird to follow. Are there any other pets around that may be intimidating her? Children maybe? Some birds are more timid and some are just lazy. Female cockatiels tend to be more timid than males and less assertive and outgoing so it may take time. Plus, she knows she can't fly and birds rely on flight to keep themselves safe, so she may be afraid of falling if she comes out so you need to make her feel safe and secure enough to venture out.
Let her wings grow back and I think she will slowly start coming out on her own, but you need to make it easier and entice her especially at first and especially since she can't fly (yet). You should put her favorite treats only outside the cage. Set up a play stand on top, or attach a long bendable rope perch in a wide u shape on top for her to comfortably perch on.
Her cage doesn’t seem to have an easy way out without her having to climb or flap and risk falling. Make it easy for her to get out. Mount a long perch from left to right inside the door midway back into the cage at mid door level and put a long wooden ladder from that inside perch to the edge of the open door extending the end into the room so she can just stroll out. Clip her treat (a piece of millet spray is easiest) to the end of the ladder that's outside the door. To prevent the ladder from falling and scaring her, zip tie one rung to the
View attachment 80808View attachment 80809side to side perch and when you shut the door just let the loose end drop to the cage floor. Here's a photo example. The cage in the photo is a plexiglas cage but it works just as well for a wire bar cage. Its like walking a plank. Set this up and give her time. She's bound to get bored, curious and tempted. When she starts to venture toward the door on the ladder, relax and let her take baby steps. Don't try to remove her from the ladder and take her out further if she's perched on the ladder. Let her go at her own pace. Before you know it she will look forward to the door being opened and the ladder being propped onto the door frame so she can just walk on out and get her treat, just sit and watch the room, climb out in top of her cage, and ultimately fly around, preferably right to you!
I use a dowel perch for the side to side perch but you can just as easily mount a thick, stiff rope perch side to side or a long natural wood branch type perch if you can find one the right size and shape. The ladder should be a dowel ladder for stability so she feels secure and doesn't fall.
Good luck!