Sounds like you are going to need a web based SMS tool, here is a quick google hit for some companies that offer that service.
From the orion side you will most likely be be setting up your alert actions as http posts to whatever web server will be ingesting them and converting them to a message format of your choice. There are also built in notification services for AWS, Amazon Simple Notification Service (SNS) Documentation , or you could send an http post to something like MS Teams or Slack.
I send my alerts to SMS through e-mail. Most carriers allow this by sending an e-mail to the number at their carrier's email domain.
There are many others as well. You'll have to look them up online. Search for "sending SMS by E-mail".
Just remember to send as plain text and keep it short! Many carriers still limit SMS to 140 characters.
When I was at my last job and everything was done via email or text message we used the same method as mentioned above.
Where I am at now we have a full paging service provided by SPOK and we are able to send more robust messages out via similar methods.