Your Air should generally plug and charge automatically at Tesla superchargers if you have set up a credit card with your Lucid phone app.
You can also start a charge by using Tesla's phone app and identifying the charging station number before plugging in.
But be aware that you'll only receive energy at a 50kW rate at a Tesla supercharger, and you'll need a NACS to CCS1 adapter.
Other charging vendors will be able to charge your car at up to about 300kW depending on car trim level, state of charge, etc, saving you a lot of time.