How do I back up my iPad Air if I can't turn it on?

Very simple - you cannot backup an iPad if you are unable to boot the device and unlock with your passcode. If you are unable to access the iPad, the opportunity to create a backup has been lost. A backup must be created prior to needing it for recovery purposes - not after.

iOS/iPadOS devices have an encrypted file-system - the encryption key being stored in the device security chip (known as the Secure Enclave). All data remains encrypted until the device is unlocked with the Passcode; the passcode unlocks the Secure Enclave and releases the encryption key to the operating system which decrypts your data.

You'll likely be unable to back it up. However, if the device hasn't run out of power or restarted since your last backup to a computer, you may be able to backup. Connect your device and see if you can initiate a backup.

Same with iCloud. Plug it in and leave it overnight. If you've been backing up, it may do so again.