Possibly TMI #2 questions

I gave up gluten last month and was hoping to see some improvements with my digestion. I experienced some constipation at first but I figured that was due to me drinking fruit and veggie protein smoothies everyday (adding fiber to my diet). Then I started noticing I was pooping like 3-5 times a day. Which was a huge influx for me. I used to go like maybe once a day maybe. They were lighter in color, softer, and they floated. I’ve always read that if your stool floats, it’s because you have too much fat in your diet. But I’ve been eating pretty clean. Would the fat be from the fruit in the smoothies? Or the nut butters I put in the smoothies?

Has anyone else experienced similar changes in their stool after giving up gluten?