If I mention to my landlord that I will not be renewing my lease when it ends but had
Not provided written intent to vacate yet, does my verbal count as notice?

Basically, I am just trying to determine if my landlord has the right to start showing the property. I have no problem with them showing and understand why they would like to, but I wasn't ready to give up my privacy yet and didn't think I would need to until inhad given them my 30-day notice -- not the three month "notice" I may have inadvertently given them by letting them know I would be moving out of state at the end of the lease

First, make sure your lease specifies that you give a 30 day notice of non renewal. Some leases require longer periods.

Second, it is not binding on you. Until you are required to give written notice, you can change your mind. However, a verbal notice is certainly enough for the landlord to start showing the unit. They have to give you reasonable notice that they will be bringing someone and you have the right to say when it would be convenient.