So u have a functioning alternator giving out a decent voltage but a bit high for normal idle speed, and if your volt meter is reading correctly.
Output current is dependent on the load drawn from the alternator, so a higher load equals a higher current and a quicker the charge, but not a full 100% charge, only a stand-alone charger will do that.
U don’t say how old your battery is, but a smart charger should revitalise a failing battery, also some alternators can be be repaired by simply replacing the diode pack.
I’m lucky with my disco if the engine starts after being stationary for three weeks, thats with a three year old fully charged battery fitted at the start, a fully charged seven year old standby battery lasts just two weeks when fitted to the disco, that why its now kept as a spare… just in case.
A five year old newish car I have will zoom into life after standing untouched after two months plus, thats the longest I’ve left it standing unused (during lock down).