You have the Jared Goff scenario stuck in your head.

This is nowhere near the same.

Goff was supposedly still developing. And then he had two poor years (he led the league in turnovers). In fact the lament among some on this board is that the Rams were too quick to jettison him because he was still developing.

Stafford is fully developed and has a looooooong track record. He is what he is. And that is elite.
There is no similar risk in extending his contract for say 4 or 5 years.

The Rams may wait until next year to extend him, but they will pay whatever it takes. And if they do wait, it will have nothing to do with seeing how Stafford works out. It many be Stafford's camp that prefers to wait. Or, for the Rams it will be about how best to manipulate the salary cap rules to their favor.