Some days it feels fine, others not so much but lately I've been changing up the strap height so it'd sit right. It's actually a good bass for fingerstyle.. most of the time, well it was crap until I set the action down. It also has a poopie-ton of high frets at the higher register, particularly at the 12th and 16th frets, which makes slides sound uninspiring as hell coupled with the shorter scale. I guess I just want to actually get better on a more jack-of-all-trades instrument. And it's not like I actually wanted the damn thing, since it was given as a gift to my dad by a distant friend I more or less don't have that much of a choice (especially when it comes to parting ways with it). For strings I use roundwounds, flats tend to exacerbate the sound qualities that I absolutely hate with violin basses. As for the amp I often practice songs through a rumble 500 lent by my dad's praise and worship group. Since it's a shared bass I don't have much I can do in the way of selling or trading it, so I'm kind of just stuck with it and have nothing better to play lol.
Fret wear and tear and even uneven frets out of the factory is something we can all run into at any point.
There are tools for leveling and polishing them. One of my basses has a high fret or two. barely noticeable but it's there. Would cost me about $40 to go get them filed down from a local luthier because fretwork and nutwork is where my ability to setup a bass ends. Probably worth doing at some point but like I say, I barely notice it most of the time.
Other than that.. string height changes dependent on gauge. Relief measurements will change dependent on the overall tension of the strings. It's not just a matter of "Cheap vs expensive" or "Round vs flat vs tape" but the amount of tension each set of strings may apply to the curvature of the neck and the relative thickness changing how close the strings are to the frets.
Each time you put on a different set of strings you should be measuring relief as well as string height, as well as intonation.
Relief is easily measured with a set of feeler gauges. Capo first fret, and fret the thickest string at the 17th or even the highest fret. What you want to measure is the gap between the string and the frets at around the 5th or 7th fret. Typically, for fretted bass guitar we want anywhere from .20mm to .50mm of relief. Which is a measurement of the curve of the neck. When you don't have enough of a gap you will get fret buzz.
If you slide the feeler gauge in flat against the 5th or 7th fret wire and the string moves, or there is not enough gap to slide the gauge in, your neck needs more relief, which is accomplished by loosening the truss rod. You only want to do this 1/8th turn at a time, tune to pitch, measure again. Adjust as needed.
If there is too much gap between the feeler gauge and frets and the string a the 5th or 7th fret, then you tighten the truss rod. (probably want to loosen strings) 1/8th turn.. tune to pitch, measure again, adjust as needed.
Tightening the truss rod straightens out the neck, pulling against the tension of the strings. Loosening allows the tension of the strings to cause the neck to curve by pulling the headstock towards the body.
This is something that is going to change every time you change to a set of strings with a different level of tension, as will intonation and levels of string height.
Another bass setup term I just mentioned is Intonation. This is basically the speaking length of the string from the bridge to the nut. You measure it by playing the open note to the most accurate tuner you have. Then you play the same string at the 12th fret. If it is sharp or flat, you have to loosen or tighten the screw at that string's bridge saddle to move it closer to, or further away from the neck until the note at the 12th fret is no longer sharp or flat. Of course, loosen the strings before moving the saddle, adjust a small amount, then tune to pitch. This may in turn effect your string height. Best you can do is adjust that, check intonation and keep fine tuning until you get as close as you'd like.
Otherwise, it might sound like you're going out of tune the further you move up the neck, because you would be.
IMO it sounds like you have some setup issues. I'd iron those out and then see how I felt about it.
In my area a proper setup would cost me about $45, not including any fretwork.