What should I do if I can't log into my MacBook Air and how can I recover lost data?

Ouch! You can try a DFU firmware Revive to reset the security enclave chip & hope it restores access to any existing macOS admin user accounts so you can unlock & access the internal SSD.

I'm not aware of any other way to reset the macOS user account password....it probably would not matter because the security enclave chip doesn't recognize any macOS user accounts which makes a password moot. On the Intel T2 Macs I have seen recovery mode not recognize certain macOS user accounts even though I could log in normally to all of them. If you have another macOS admin user account, then try to login normally with it instead. If you can do that, then it is possible to access the data within the other user accounts (with a little help).

If this does not work, then there is nothing you can do to recover the data since the data is hardware encrypted by the security enclave chip. If you cannot authenticate to the security enclave chip, then there is no way to unlock the hardware encryption. At that point, the only way to be able to use this laptop is by performing a DFU firmware Restore which destroys all data on the internal SSD & pushes a clean OS onto the internal SSD.

Unfortunately I think you just had a hard lesson about the importance of backups.

Go into recovery mode (bootup, hold 'power button' + 'command key' + 'R'), select options. Then follow to instructions (you will need your Apple ID). After that hover utilities (left-upper corner) and open terminal. Type 'resetpassword' (without the '), follow further instructions and you should be fine.

You would recover your data from your backup.

What happens when you try to login? Did you just forget your password or is some other message appearing?