Does the invoice go to ZATCA automatically, or is there a button?

Automatically. The moment you press Save (or Approve in Sales), the system sends the invoice to ZATCA as part of that same step. There is no separate send button.

• Invoice to a company with a VAT number (tax invoice): ZATCA clears it within seconds, then it can be printed and sent to the customer.
• Invoice to an individual (simplified): it prints at once, and the system reports it to ZATCA in the background within minutes.

If ZATCA refuses the data (a wrong VAT number, for example), the invoice is not saved at all, and a message says what to correct.