Width is more important than height, as budgies (and other birds) like to be as high as possible. Flight cages normally have a good amount of both height and width, and are a nice rectangular/square shape, which is best for a bird cage. For a single budgie, I would look for something like this, or if you have a tighter budget then this is also a good sized cage, with much more width than height. Also, make sure that there isn't more than half an inch for bar space.
My personal cockatiel wish-list:
Tops 25 lbs Pellets: https://topsparrotfood.com/products/tops-mini-pellets?variant=16280835162155
Yaheetech 54-inch Wrought Iron Cage: https://www.amazon.com/dp/B07MXSRL2Z?ref_=cm_sw_r_cp_ud_dp_TH9DCG57P6GDJT88ZATV
Gram Scale: https://www.amazon.com/dp/B09QFWXSD8?ref_=cm_sw_r_cp_ud_dp_6VMQSFK0BB11S5N76FWQ
Bird Stand (For Gram Scale/Stationing): https://www.amazon.com/dp/B08L66L5BZ?ref_=cm_sw_r_cp_ud_dp_ZNMMVANYWQSAQ75X99FD
Shower Perch: https://www.amazon.com/dp/B0040Q85L6?ref_=cm_sw_r_cp_ud_dp_9NTF334W9ME1GSPA70PS
BirdTricks Tiny Toy Box (8 Toys): https://birdtricksstore.com/collections/premium-parrot-toys/products/tiny-toy-box
Bird Harness: https://www.amazon.com/dp/B082XXF8LD?ref_=cm_sw_r_cp_ud_dp_YA1BT9ZTBJCKH3AEJ7Q2
Subtotal for all items: $361
Hand-Tamed Cockatiel: $200
Vet Emergency Budget: $500
Total: $1061
Conclusion: You have to be ready for these types of costs and you also need to study how to understand bird body language and how to train birds using permission based training.
Cockatiel Training 101: https://youtu.be/HRjsVO4zcmo
BirdTrick's Free Guides: https://birdtricksstore.com/collections/free-products
Good luck!
ah, a houdini birb. for the future, definitely do start saving up (or whatever you need to do) for the new cage with smaller bar spacing because safety is definitely a concern when she tries to squeeze out. it’s expensive but here’s a big enough cage with 0.4” spacing instead of the typical (and usually enough to prevent birds from getting out) 0.5” https://www.amazon.com/Yaheetech-Standing-Parakeet-Cockatiel-Lovebird/dp/B07MXSRL2Z/ref=pd_aw_ic_dpcp_m_1_m_1?pd_rd_w=tRNCF&content-id=amzn1.sym.dada13db-73d7-44a3-a41c-a737643880d1&pf_rd_p=dada13db-73d7-44a3-a41c-a737643880d1&pf_rd_r=0J2HYA4XEPTMVH8K5A29&pd_rd_wg=dr6nR&pd_rd_r=d0a0011a-1e46-4eb0-8feb-ee6081da881a&pd_rd_i=B09NPWKJMV&th=1&psc=1#aw-udpv3-customer-reviews_feature_div it has some guillotine style doors so you’d just have to put a clip on them to prevent her from sliding them up.
As for now…
how big is your cage? what is the current bar spacing?
regardless, a cage is still a cage. my budgie has a huge flight cage with lots of perches and toys, but when he got an injury and the vet said he should stay in the cage for a few days to rest (instead of his usual being out all day) he looked so grumpy and would climb all over the door wanting to be let out whenever I looked at him 😭
i’m sure if you lived in a mansion you’d still want to get out of the house once in a while!
even if they don’t seem to want to get out, giving them the chance to may be good for them and is important to their well being. she’s trying to escape, so obviously she wants to leave sometimes. if you leave the cage door open, then maybe she won’t feel like trying to dangerously escape? it can take time for them to want to come out. heck, most of the day my bird will just sit content on a perch right outside the doorway of his cage. but he’s less antsy just having the choice of coming and going.
try putting perches and toys on the outside of the cage to entice them and give them more usable space. give them millet in the doorway of their cage, and then slowly make them have to start going further for it.
as for flying concerns, it’s good your birds are unclipped. she may just need more experience flying if she isn’t out a lot and gets put back in in fear of her getting hurt. I know it can be scary to watch them fumble, but making the room less dangerous and giving her the chance to practice will make her less likely to hurt herself. make sure ceiling fans are off, and offer lots of spots to land around the room and near walls so she doesn’t crash into them. closely supervise her until she gets better, but still give her the chance to figure out the room.
start by bird proofing your room so it is safe when they are out, whether intentional or not. then start leaving the cage door open often. they can go back in for food as they please, and being able to fly and play outside will make them more experienced/less likely to frantically fly and injure themselves, AND happier and less likely to engage in dangerous, boredom induced behaviors.
give Owen a chance for a bit longer :) even if you get Penelope a different friend, you will have to work on getting your birds out of the cage for a while every day anyway.
I got it off Amazon here's the link Yaheetech 54-inch Wrought Iron Standing Large Parrot Parakeet Flight Bird Cage for Small Parrot Cockatiel Sun Parakeet Green Cheek Conure Lovebird Budgie Finch Canary Bird Cage with Stand https://www.amazon.com/dp/B07MXSRL2Z/ref=cm_sw_r_apan_i_42R4MHYN7AX7CEADCSEY?psc=1