slow charge -- 2 amp manual 12v charger

You can't do much "damage" to the battery with a charger that only has a 2A capacity. If it was left running for several days beyond the full charge point, that might force an overcharge. As the battery increases its level of charge, the charging current will automatically diminish as the charger typically will not produce a charging voltage above a safe level.

Further, does the charger know that the battery is question is AGM and therefore has a higher voltage requirement as compared to a regular 12V battery? If the charger does not make that distinction, then it is likely the charger will call the battery fully-charged before the battery is actually charged.

I believe you have a digital multimeter? If so, when the charger indicates the battery is fully-charged, measure voltage across the battery with the charger connected. Then set the multimeter to measure current and put the meter in series between the charger and the battery, to see what the charging current is. "Series" means: disconnect the charger's positive cable, attach one meter lead to that cable, then attach the other meter lead to the battery's positive terminal. Pls report both findings.

Worrying about a 12V battery being overcharged is somewhat like worrying about having too much money, or being too attractive, or being too smart. There are very few who need to have such concerns.

Usually the reverse is the problem. In the case of the battery, most 12V batteries spend their lives in partial discharge which results in a shorter service life than necessary.