Is there any other way to say 'Sent Successfully'?

The actual message is 'Message was sent successfully'. But, we are not sure that the message was delivered to the person or the person has read the message. Is the use of 'sent successfully' correct?

Yes, the use of "sent successfully" is correct because when we talk about sending messages, we only refer to the action of message being sent from our location / email etc.

This does not include notifications regarding delivery or message read receipts.

There are separate features and thus separate messages for such notifications.

For example:

"Your message has been delivered" (Confirming delivery to the recipient)

"Your message has been read" (Confirming that message has been read by the recipient)