Can you email someone after they bought from you?

Usually Yes, Within Limits. Most regulations allow transactional communication related to purchases. Many also allow limited marketing to existing customers under implied consent or legitimate interest provisions.

CAN-SPAM allows commercial email with unsubscribe. GDPR allows legitimate interest as basis for some customer marketing. CASL allows implied consent from purchase for 24 months.

The extent of permissible marketing varies by regulation. Transactional messages about their purchase are generally fine. Broad marketing requires understanding specific regulatory provisions.