SMS is sent within unassigned space within management frames.
Cell works kind of like ATM - Asynchronous Transfer Mode, which unlike packet-switched networks, continually transmits frames (even empty ones), as a means of ensuring stable, performant delivery.
Like ATM, cell kind of does the same thing (that is, when it makes a connection).
Within those frames are segments which are allocated for different purposes, someone got the great idea to transmit bits within a segment that wasn’t yet assigned to anything by the standard.
Those segments can hold… 160 characters (IIRC), and for technical reasons, this became 140 characters (again, IIRC).
So whenever your phone pings a tower, those frames get sent. From a bare transmission perspective, there’s no additional cost. The cost is on the backend hardware that extracts the SMS and the routing of it. So there’s some cost, but at 10 cents per message, there’s got to be 9.9 cents of gross profit (just guessing).