Tighten the screw appropriately. You may need to replace with a shorter screw if it ”bottoms out” before it snugs it up. Cheap knobs often do not have gripper prongs on the knob, and have generic sized screws that either have to be cut or replaced.

Get new knobs before others start to corrode.

Here's a link to find a knob without that black erosive ring. https://www.hardwareresources.com/decorative-hardware/cabinet-knobs-pulls.html

The knobs shown must be quite loose, to wobble enough that the wood is so worn.

I'd remove it, touch up the paint with white paint and a small brush, and re-install with appropriate length, well tightened screws and - if the problem persists - look into "tooth lock washer". Or replace pulls with a different design.

" I installed these kitchen cabinet poles and when they rotate "

They are pulls, they are not supposed to "rotate".

All the holes were installed tightly. They loosened up overtime. How do I prevent them from getting loose? And from rotating? Every time they rotate, it strips off some of the wood. The polls were never loose when they were installed, I just loosened them a bit to show the damage that it caused on the wood Outside of the footprint of the pole, which is what creates the problem as you can visibly see the eroded paint.

Part of your problem is the style of knob you have. With the horizontal pull, any movement will make it not level. If it were round, movement would not matter. We used square knobs in one kitchen. They never stayed square. Switched to round and not a problem. You may be able to tighten with blue Loctite thread lock.

As someone else suggested, add a lockwasher to the screw that holds the knob to the drawer. That will help the screw to hold the knob tight against the drawer to prevent it from rotating.

Tighten its screw whenever you feel a knob has loosened. I have to do that occasionally and I don't have T-shaped knobs that are easy to grab and inadvertently twist.

Blue (not red) Loctite will keep the screws tight. The problem is that even with screws tight, nothing stops the pulls from rotating except friction. Go to a hardware store and get some thin "tooth lock washers" and try those out. Note the tooth washers will dig into the wood, and may be (barely) visible. If you don't want that, then change pulls.

Here's the link to a new knob similar to yours. I have bought many of pulls & knobs from this company with success for my clients over the years. You can request 1 free sample to try & inspect beforehand.

https://www.hardwareresources.com/decorative-hardware/cabinet-knobs-pulls/knobs/48.html

There's a lot of cheaper hardware out there where they "cut corners" on quality, for example materials that corrode, screw threads that wear over time & or screws made out of softer metal that strip.

It's also a challenge to put a flat screw tight on a curved area, like raised panel cabinet doors. So, it's extra important to get strong, quality screw threads that can handle it.

In regards to the dented areas on the drawers, you may want to get different knobs with a wider base for the drawers to cover the dents, which compliment the style you have on doors. I would get a few samples, & see if it covers the dents & you like it first, then order the rest. Here's a link to see an example of a wider based knob to get started finding something you like. (note: the wider base knobs with the wider flat surface will be a challenge to secure flat on the curved area, so get a few samples to test to buy the rest in confidence) https://www.hardwareresources.com/decorative-hardware/cabinet-knobs-pulls/knobs/449.html

Another idea to hide the drawer dents, is to cover it with a cup or backplate.

Note: the backplates will make an indention in the paint over time, so choose something you really like. I do not recommend these unless it's to cover dents in drawers due to the indention.

This is just an example of what backplates are.

This is an example of cups for the drawers.