"Go outside on a sunny day, put the camera in green square and take some images of something 10 to 15 feet away at several focal lengths."
I like that suggestion a lot but I need to add a little more advice to it. First reset the T6i, Menu>Tools>Clear all settings and Clear all custom settings. Now choose P mode in favor of the green square. Set ISO at 200. Average WB. Use One Shot never use Ai-servo for this test. Make sure the lens is set to AF.
Now do the test outside on a sunny day. Shoot various subjects, trees, buildings, landscapes, people, etc. Make sure you run through several different zoom settings, I.E. some at 18, some at 35, 50, 100 and 200mm. You know use them all. Don't change anu fo these settings until you are done with the test. If it works and all looks great there is nothing wrong and you had a setting wrong or your technique needs work.
Pictures done at the 200mm end and a rather slow SS of 1/60 for instance is a prescription for blurry shots. Fast motion and a slow SS = blurry photos. Not holding the camera steady, all will yield blurry shots.