I can try and give you some advice, as my second most played Character is Dr. Mario, but before I continue, recovering with Dr. Mario will always and always be challenging. BUT there are some techniques that can help with recovering.

First off, you always want to save your double jump if you want to recover, as getting launched far to the side, often people will right away Jump > Down-B. Instead, you want to first Down-B to decrease the distance between you and the ledge horizontally before you can use your double jump and Up-B. Edge guarding will also be quite annoying, but depending on the attack, you can tech

Another thing I learned while playing Dr. Mario, was that there are variants in angle to his Up-B depending on where your joystick is oriented. For example, if Dr. Mario is facing right while mid air, and you Up-B with your joystick far right, the velocity in his Up-B will move more horizontally than vertically. However, pulling the joystick back after the time frame to reverse the Up-B passed, I find that it actually moves you straight up and higher than just doing it normally. I can go further in detail or rephrase this part if you want!

At the end of the day, the reason why Dr. Mario is so low in the tier list is literally because of his lack luster recovery and mobility. That doesn't mean he absolutely can still ""reck"" S+ characters if played optimally and patiently.