Despite what your operator or has published, the thread is the wear indicator for the tire installed by the manufacturer for the purpose of indicating a tire is approaching wear limits. Retreads often end up installing a new thread layer so multiple are possible. The further you wear a tire beyond the indicator the more expensive a retread gets.
Is it safe to operate a tire with thread showing? yes..
Is it legal to operate with no groove or thread showing? Up to the aircraft manufacturer and your operator.
I can defer a tire with exposed thread until it gets to the 1st cord or earliest available ground time on multiple aircraft types with my operator.