Is this problem likely to be fixed by replacing the trackpad?

My main system is a 2019 16" MacBook Pro. The trackpad has occasionally been "sticky" (not reliably sending a mouseUp event after a tap) ever since I bought it, but it wasn't bad enough to be worth the two-to-five-days Apple would take to service it, so I didn't bother. My AppleCare on this machine is long expired

The issue is starting to reach the annoying stage now. What happens is that I have my trackpad set to "Tap to click", because the amount of pressure it takes to activate the trackpad-as-button is, for me, excessive. Sometimes, unpredictably and inconsistently, when I lift my finger after a tap, it doesn't release the mouseDown event with a mouseUp, as if I had double-tapped to get a drag-lock.

Recently, the frequency of this behavior has increased, and I've started to see situations where single taps are being treated as double, triple, or even quadruple taps, sometimes spaced out enough that they actually count as separate clicks rather than double-clicks (or more).

I don't see any indications that my battery is swelling, like I did the last time I had trackpad issues (on my 2010 17" MacBook Pro, when it was about the same age as my 2019 is now), and the fact that this symptom has been showing up intermittently since I got the machine suggests that even if the battery is swelling and exacerbating the symptom, there's still likely to be an issue with the trackpad.

I am about 75% certain that it's not a software issue, but it's hard to be sure from my end. The issue doesn't manifest if I turn off tap-to-click, nor does it appear with an external mouse or trackball. I don't have access to a Magic Trackpad to see if that would have the same issue.

I've looked over the guide for replacing the trackpad, and things are a lot more complicated inside this machine than they were in my 2010 MBP. It will also require a lot of new tools that I don't currently have, at a not-insignificant cost. So I'm hesitant to try this repair without being reasonably sure that it will cure my problems.

Ultimately, my question is, is there any reasonable chance that this problem is caused by something other than a defective trackpad (and exacerbated by a possibly swelling battery)? Or is it probable that replacing the trackpad would do the trick?

For that matter, would I be better off just buying the Magic Trackpad? A replacement trackpad and cable runs $92 here, plus the cost of additional tools that I'd need, and my time doing the repair. A Magic Trackpad is currently $149. (I greatly prefer a trackpad's flexibility over other pointing devices.) I already have an external keyboard I can use. I rarely use the Touchbar, and I no longer take this laptop anywhere, so portability isn't an issue. (Once I can afford it, I'm planning to replace it with a Studio.)

TL;DR: My trackpad has been acting up since I got the machine, and it's getting worse. Will a trackpad replacement fix it? Is there likely something else going on? Or should I just get a Magic Trackpad?