Annihilation of Shiite dynasties doesn't equal annihilation of the Shiite community as whole. And an Ottoman Persia as the end would mean a failure Safavid revolution, hence preventing the was Sunni majority Persia being mass converted into Shia by the Safavids. A minority Shia community, even if rather sizable, would mean no harm for the Ottomans because they would be simply not powerful enough, especially because now Persia is already under Ottoman control.
Besides an anti-to-a-particular-faith Ottoman Empire doesn't really go with the nature of the empire its self. IOTL where there was a successfully established Safavid Empire, Ottoman Empire remained fairly tolerant towards the Shiites, as it was towards any other religions and sects. How much likely is an anti-Shiite Ottoman Empire in a world without any threatening Shiite power towards them compared to this reality?
One more addition, is also that before they were "unified" by the Safavids, the Shiite Persians weren't very united themselves. When Persia is finally under Ottoman control, it'll be most likely for us to see the Ottomans keeping the Persian Shiites disunited by tolerating their existence and guaranteeing the safety of the very each Shiite sects from each others' threats, rather than antagonizing them which will make them unit under the single anti Ottoman banner. But Ottomans would going to have the support from the rest of majority Sunni population against them anyway.