Strip it with a heat gun. Then prime properly with BIN shellac, and paint with a good quality trim paint like BM Advance.

Pictures?

When painting trim, I go one step up in sheen (usually semi-gloss) and go over my brushstrokes with a small foam roller.

Maybe it can be sanded smooth and repainted post pictures to see what you are working with

absolutely terrible paint job dine on the kitchen counter trim.

Pictures.

Because I don't know what 'kitchen counter trim' is. Unless it is edgeband? Something like this?:

If this^^, then it should not be painted at all.

Here is a picture. It is even worse on other parts of the counter.

It's just everywhere. I can't afford a whole kitchen remodel right now. I guess I'm just hoping to make it look not horrible in the meantime while I save up to remodel.

How are your woodworking skills? Honestly, I would probably just pull that and put in new. The wood looks really rough and it will be hard to strip it and redo.

A new Formica counter should be pretty affordable

Maybe I'm missing something. The trim is a mess. That doesn't, in any way, mean a remodel is the way to correct it. It's trim. Fill, sand, prime and paint or replace the trim (and paint).

By "remodel" perhaps you mean, "replace trim" and not "remodel kitchen". If you are speaking only of trim and don't wish to replace it at this time, yes, repair it and paint it.

Remove that and replace it. Sand, fill, sand, prime, sand, prime, sand, and paint it gloss black. It’s far easier than the even more hours of work required to get that existing to adequate status. Black is what will blend with the counter and disappear, but its also what takes the most work to make look good.

Easiest to replace with new Formica counters. Either stock ones from the big box or even scout Marketplace & Craigslist for used ones. You can find them for free or very little cost where folks are pulling them out & replacing with stone counters.

Measure your base cabinets first & make sure they are somewhere around standard depth (24") .Standard stock laminate counters are around 25-26" deep.

Or, for least amount of money, either replace the trim or invest in an orbital sander and clean up what you have. Fill, prime & paint.

I have a Bosch orbital sander and like it a lot. https://www.thespruce.com/bosch-palm-random-orbit-sander-review-4771166