A state machine with flip flops is simple to control these 3 states. plus Vbat present.
Use a current sense R such as 75~ 100mV at max current.
Use a band gap ref for controlling current , voltage and shutdown float, which is included in LM317, but using a linear regulator is very inefficient with heat sink required.
Measure average current with a comparator to turn on MOSFET for CC mode with series storage inductor and clamp diode to make a buck regulator. This will make it oscillate, so inductor must be able to handle DC current. ( e.g. 50~100uH)
Voltage feedback also feedback to prevent over voltage with small filter.
When CC reaches 7.2V it goes into CV mode and a few seconds after CV mode, it checks if current is less than ~ 10% of max rated current, then can go into Float mode.
Generally VRLA's use a thermistor to compensate target voltages to prevent gassing according to Mfg specs.
Or look for a ASIC to reduce component count.