I used TurboTax to file a federal tax extension. It was easy and automatic. Does TT also file state tax extension?

See this TurboTax support FAQ for state extensions - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-extension/need-file-extension-personal-state-taxes/L32Mt8ZNv_US_en_US?uid=m8x7fp7e

You can't file an extension for your state through TurboTax but we have instructions for each state that you can use to file an extension for your state tax return. You can click this link: How do I file an extension for my personal state taxes?