The battery uses coulomb counting to assess state of charge not the terminal voltage.
There is a hall effect current sensor in the negative battery lead and if you charge the battery with a charger on the battery terminals the electronics have not seen any charge go into the battery so the terminal voltage could be 14 volts and the electronics would not be happy. You are in a no win situation at present, the battery is fully charged but because the sensor was bypassed when you charged it the electronics did not see any charge going into it so will not let stop start system operate. I do not know whether there's is a reset that Honda dealer can do, but as I said a page from Honda technical bulletin was posted on this forum telling technicians to only charge stop start battery with negative charger lead clamped to car bodywork, not the negative battery terminal.. which bypasses current sensor.
Smart external chargers use voltage to understand the SOC, some professional devices measure the voltage before and after appliyng a heavy resistance for some seconds used to simulate a startup; if the gap is big, it doesn't matter if the initial voltage was high, this means the battery is out of order.
Our Hondas use coulomb counting for sure, but I'm pretty sure this is not the only parameter used; maybe there are some equations as "
after X current sent to the battery the voltage must raise not less that Y in Z minutes; if Y is lower and/or Z is too long, the battery is not OK". Or "after a restart, the gap between initial and final voltage must be lower than R" and so on. Coulomb counting cannot be the only parameter, otherwise the car would go on showing the alert even after a new battery.
And there is this strange behavoiur: starting my car in the morning, I see that initially S&S works fine but after 5-6 times it stops working, with the battery alert on my dash. I was thinking this was due to many current drags, but I noticed this happens also after starting and running for 40-50kms in a highway, without S&S and when the battery should be well charged (no restarts and many minutes with high rpms), and strangely I see the battery alert at the first stop. So why battery conditions are good after five minutes from startup (S&S working) but they are not good after 30 minutes in a highway? Maybe the system reads a good voltage on startup, but it does not count enough recharging current?
I'm tempted to leave the battery leads disconnectet for a whole night, just to see if this could "erase" the coulomb counting memory, just to try...