Which BIP describes the structure and algorithm for creating a wallet file? My app is able to create a public and private key from BIP39. The uncompressed private key is concatenated with a sha256 (private key) and then encrypted via AES and saved to a file. To decrypt, you will need to decrypt the entire file, then take a hash from the first order of bytes and compare with the second half.

I plan to add support for BIP32, 43, 44 and am already working on it, but I am faced with the issue of storing information for creating backup.

My way of creating a file is not suitable, so I’m wondering if there is a ready-made BIP to solve this problem.
There is a list of BIPs at https://github.com/bitcoin/bips

I don't see anything that specifies a wallet format. 

To be honest I'd be surprised to see one. This is something that each implementation ought to determine for itself, Some wallets might use an embedded SQL DBMS, some a Berkely DB format, some a JSON store of some sort and so on. Similarly, the contents may depend on what unique features and facilities the wallet offers. Wallets might be multicurrency or even multiuser, they might have settings for GUI skins that need to be saved as part of a wallet backup, they might have IDs for associated exchange or other services.