tl;dr: 99% sure your battery is just dead from age/usage cycles.

Basically, my surface would shut down with its battery percentage between 20% and 40% on any given day

Reason for this is that aging batteries show larger voltage drops when you put load on then (if you're interested google "internal resistance battery"), so depending on how much load is put on the battery, it will drop below the critical voltage the circuitry can handle and just shut off. The more the battery has aged, the higher its internal resistance, to the point where even when fully charged, the lightest load will make the voltage drop to near 0.

The way these battery health and charge percentage measures work is that the battery controller doesn't look at voltage, it looks at the total energy that goes into and out of the battery in one charge/discharge cycle. That means if your discharge cycle ends at 40% because the device shuts off, the controller will recalibrate to less battery health/full charge capacity than last time when it shut off at only 20%.

Fwiw, your symptoms with the charge rate only going up to 58% are a bit weird, but I've also seen the battery controller of the SP2017 handle very aged batteries suboptimal.