Epever boost cut-in difference between 2 models

Basically just hook up any 12v load with a known wattage. A 12w bulb, for example, is ~1a at 12vdc. Your battery is 100ah, so it should run the bulb load for ~100 hours to a 0% SOC. You don't need to (and shouldn't) drain it that far though, just far enough to get an estimated capacity. If it takes 100hrs to drain, it should take ~10hrs to get to 90% with a voltage ~12.5v. If it gets there in an hour, the battery has lost most of its capacity.

If available, something that draws ~5% of capacity (so 5a or 60w in you case) would be ideal. A larger load can be used, but voltage can sag under load then recover to a better SOC indicative voltage.

Chart of battery voltage vs SOC (and other useful info:

https://www.solar-electric.com/learning-center/batteries-and-charging/deep-cycle-battery-faq.html#Battery Voltages

You can also get automotive load testers like
http://www.canadiantire.ca/en/pdp/motomaster-battery-load-tester-100a-0113003p.html

These testers may be misleading for deep cycle batteries though, as they're designed to measure instant power available for engine starting applications (cranking amps), rather than capacity (amp hours). If you happen to have one around or can borrow one, you could try it as a rough indicator of battery health.

I suspect you may be right about the SOC being out of whack. If voltage stayed above 12.8ish overnight with no charging sources at all, that suggests the battery may be ok.

SOC can be tricky. It's likely estimated based on current and/or pwm duty cycle of the controller. Once it starts charging, it takes account of how much it takes to raise the voltage over time. There are lots of variables, so we generally treat them as rough estimates only. Accurate state of charge requires either measuring specific gravity of electrolyte (most accurate, but not possible for AGMs), or resting voltage (still pretty accurate, but battery needs to be left with no loads or charging sources for several hours.

Where are the voltages coming from (ie measuring with a multimeter at battery terminals, charge controller output terminals, or?). It might also be worth checking these
connections. A wonky connection could account for some wierdness in the controller.

It's probably good to run the battery down to about that level periodically anyway, if only to be confident it'll be fit for purpose if/when needed for an outage.

I guess there might be a sort of "learning" algorithm in the controller, but I'm doubtful. Did you enter any of the variables like bank size (ah) or charge efficiency (%)? To learn meaningfully, the controller would need to be able to differentiate between current going to charge vs current used by loads, which would require a DC shunt (typically on the battery negative connection). Some controllers do use shunts, but I'm guessing yours doesn't. Even controllers that do this (mine do, but mainly to control transition to float) don't have particularly accurate SOC.

As a lead acid battery gets full, the current required to hold it a given voltage drops off, regardless of current available. Depending on depth of discharge and charge rate, this starts at about 80% full. It continues to drop off on a curve until it gets to ~1-2% of capacity, at which point the battery would be considered full. In this stage of charging, the controller "pulses" pv current at pv voltage to the battery as often as needed to hold the battery at a given voltage (15v in absorb/boost in your case). As the battery gets fuller, the time between pulses needed to hold the battery voltage gets longer. My guess is the controller is estimating state of charge during this stage of charging based on the timing of these pulses.

When solar kicks in, these pulses would be longish as voltage is raised from overnight voltage to 15v, and the controller is likely reporting SOC on that basis.