This problem can be fixed in many ways. The methods I use involve the controller being fully disassembled and having the analog sticks exposed.
The first fix can be as simple as cleaning the analog sticks with either alcohol or some kind of electronic contact cleaner. The second option is to pry out the potentiometer that is causing the stick drift (each analog stick has two, one for up and down and the other for left and right) and clean it with a lint-free swab and some kind of cleaner, or replace the wiper if it is ever damaged. If the carbon tracks on the inside of the potentiometer is damaged, you'll need to replace them by buying replacements online, either the wipers or potentiometers alone or the entire stick module, which is what I recommend. You can buy official replacements on a site known as Mouser Electronics and search up ALPS RKJXV if the stick modules are green or C&K THB001P if the sticks are orange and black for a couple bucks each. You can look up tutorials online, but in order to do this repair, where you need to replace the potentiometers, you'll need soldering gear such as an iron, solder, flux, and a tool to remove the solder and component in order to replace the sensors. Even though I've only done this fix for DualShock 4 controllers, it should be the exact same for the Dualsense controllers since they use the same stick models. I hope this helps!