I don’t compete so no recommendations on best comp shoes. Generally for squats I like minimal cushion, but not too close to barefoot and have been using NB minimus shoes. I think there are some that argue for squats some cushion is good.
Deadlifts though, I like barefoot (though you never know what may be lying around in the garage gym, and if you are in commercial gym they may require some type of foot covering). However, I have just recently been using basically a “slipper” that you can remove the sole insert if wanted (Slingshot) and have really liked those…really cheap too. The alternative is socks only, but believe I would burn through those fast when compared to the slipper that has some fairly durable rubber traction at the bottom.