Can the stick drift be solved?

You can open it to “fix” it, but you cannot “solve” it.

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!

If you want a more involved solution, it's possible to replace the thumbsticks with hall effect sensor versions (search eBay / Amazon for some examples). I am currently trying this with my V4 controller and have managed to test this wired to the PC and it seems to be working really well (can't connect to PS5 yet as I have Bluetooth issues).

You do have to solder the thumbsticks onto the board and taking the old ones off is difficult unless you have a hot air rework station, but in theory the replacements should never drift as the parts have no wearing contacts. Many people have had good success. If can can fix my Bluetooth issue, I'll report back on how things go over the next few months,

In the short term you could try to recalibrate the thumbsticks if the drift isn't too bad. Here is the site that you can go to for it: https://dualshock-tools.github.io/

Yes the stick drift can be repaired.

I recently fixed my horizontal stick drift, but unfortunately I caused another issue.

As I was cleaning off the sensor of my right analog stick I took out the wrong sensor by mistake. I thought the right sensor was for horizontal movement and the top sensor was for vertical movement. I was so wrong.

As i put everything back together I was able to smoothly fix the horizontal movement, but really messed up my vertical movement. I tried repairing it again but the plastic holder broke off from the 3 solder points.

It was dumb to assume, but that's why we learn.