You cannot really tell the AH of a lead acid battery without discharging it some amount. The closest, damage minimizing test, is to discharge it by about 30-40% of expected AH then let it sit for a couple of hours to allow battery to reach equilibrium rest state. Then measure terminal voltage and check it against expected SOC open circuit voltage.
If open flooded cells, best test for SOC is measurement of specific gravity of electrolyte. Cell voltage is very close to SG +0.845 volts. 2.12v rested voltage is a fully charged cell with SG of 1.27 to 1.28 at 25 deg C.
90% SOC = 2.103v, SG = 1.258
70% SOC = 2.062v, SG = 1.217
50% SOC = 2.017v, SG = 1.172
The charger could measure the rate of rise in voltage with a given current and adjust its rate based on voltage rise. The issue with this is it only works if battery is good. A bad battery may rise too quick if it has high internal resistance due to grid corrosion or too slow if there is high internal leakage.
For a three phase charger, the first constant current phase should be maintained until battery reaches bulk voltage (14.3-14.5 vdc for a six cell battery). Typical maximum bulk current rate is 10-15% of AH rating. An AGM battery can go to 25% AH rate. It then maintains bulk voltage regulation until current drops to about 2-5% of AH battery rating. Alternate approach is to just time the absorb constant voltage period. If current termination is used there should still be a max timeout to prevent a battery with high leakage never making it out of absorb due to current never dropping to 2-5% AH level.