Yoga is usually done in sports clothes, barefoot and on a yoga mat. Yoga clothes are suitable for yoga, the same as for fitness and for physical training. The main thing is that the clothes should not constrain the movement. More information here: https://www.julianalucky.com/post/mommy-and-me-yoga-benefits.
A yoga mat is needed to keep your feet and hands from slipping on the floor, as well as to make the surface for classes softer and more comfortable. Special mats with a textured non-slip surface are used for yoga classes. This is necessary for comfort and safety, as slipping can cause injury. In addition, if you have sensitive joints, you will not feel comfortable practicing on a hard and cold floor.
Many yoga studios use additional equipment and inventory. For example, bolsters, blocks, belts, chairs, and blankets. You don’t need to buy any of these to start doing yoga. If you’re going to take a class at a yoga studio, they’ll provide you with everything you need. But if you’re practicing at home, you’ll definitely need a yoga mat.