Hi Bob and welcome to the forum. Regarding starter batteries remember they are consumables. I wouldn't be too concerned with age either since it's possible to ruin a typical lead/acid battery in a matter of months if it's not charged adequately on a regular basis.
Another point is that Morgan cars are often used sparingly and/or laid up during the winter months. Leaving the battery on a smart multi-stage charger in such situations offsets their degradation due to loss of capacity but is still not optimal.
Batteries thrive on being used so an easy starting car used regularly throughout the year will provide the greatest longevity. Six to eight years is a typical span for one well looked after. Some claim as much as twelve years but that's nothing to be proud of, it simply means you're sailing closer to the inevitable day there is insufficient capacity to turn over the engine, typically when winter temperatures strike.
Measuring the voltage across the battery a few hours after use gives a good indication of its state of charge (SOC) but since this is only within the confines of remaining capacity, it's not always that helpful.
Most Morgan's should survive three weeks at least without charging. If in doubt though leave it on a smart charger with float mode if it's going to be unused for longer. This in preference to those who use a battery kill switch. Modern cars have adaptive mapping within the ECU and this will lost with battery disconnected so the engine will have to re-learn which may take some time to optimise. Car radio's loose station memory similarly.
Finally please stay clear of old style "battery testers" since they put a brutal load on the battery which may achieve little more than finish it off and at best may take a chunk out of its life.