I just filed my state return. The turbotax fee shows as pending per my bank BUT Turbotax now shows my state return as "started" not "filed" - what is the true status?

You didn't say anything about the Federal return.  I assume that you must have already efiled the Federal return previously and that it was accepted.   Otherwise, it wouldn't have let you try to efile the state return.

Were you wanting to efile?     Once a return has been efiled (actually transmitted), the status at the Tax Home page will change to one of these:  pending, accepted, or rejected.  If the Tax Home still shows the status of the state return as "started", then it has not been efiled.   

Paying is not the last step in filing.  After paying did you continue on through all the remaining screens until you got to the final screen that has a "Transmit My Return Now" button and click it?   If not, you can go back and transmit it.  You should not be charged again.   In the unlikely instance that you were, that can be corrected by Support.

Once you successfully efile, you should also get an email saying the return was successfully transmitted.  That should be followed by a second email (often 24-48 hours) about whether it was accepted or rejected.