URGENT help please not sending emails

Hello, the problem I’m facing is that the automated emails that my WordPress website should be sending out to admin and users (for example: Password reset request, booking request, etc.) are not going out.
They worked up to a couple of weeks ago. As of now, not anymore.

The website is → https://passionforpuglia.com
Theme used → WP7Rentals
Plugin used → Postman
E-mail address those automated emails are supposed to be sent out → info@passionforpuglia.com

I’ve been told this is these 2 errors
Error this week : gator4240.hostgator.com has timed out - https://postmansmtp.com/office365-smtp-connection-timed-out/

Error last week : ERROR PostmanWpMail: Exception code=535 message=Incorrect authentication data https://postmansmtp.com/incorrect-authentication-data/