Emails stuck in Email Queue

By default when you send an email through frappe.sendmail() By default value in that function is delayed=True
For send an email instantly without being in queue you can just pass delayed=False

frappe.sendmail(
    recipients=recipients,
    subject=frappe._('Birthday Reminder'),
    template='birthday_reminder',
    args=dict(
        reminder_text=reminder_text,
        birthday_persons=birthday_persons,
        message=message,
    ),
    header=_('Birthday Reminder'),
    delayed=False
)