I think only you can decide if it is worth your time and money to take it out and get it charged compared to purchasing a new battery.
To assist, if we assume a car battery will last 5 years, and you have had it for, say, 1 year, then you would expect this battery to provide another 4 years of service which I'll say is a value of 80EUR.
But if, as others believe, that this battery has lost life then you may not get another 4 years of service - without any justification, say you only get 2 years of future service, compare your time and costs against a battery with a value of 40EUR.
Re 2V: it would be odd that with load removed that you are getting 2V. This suggests that 3 of battery cells have gone reverse polarity or that 5 cells are shorted or some combination (I will not consider shorted cells beyond this point since, without justification, I will deem to be terminal).
Given that this took place over 1 month, then there are 2 possibilities:
1) your car has some fault that is discharging battery; or
2) your car's quiescent current is high and flattened battery; or (again)
3) some combination.
if 1), then you might want to recover this battery to allow you to determine if your car has a fault (eg. boot light stuck on) before you invest in a new battery and have same issue.
if 2), then since battery current has been low, then 3 weaker cells have been reverse charged by stronger 3 cells. If this current is small, then recharging your battery will re-reverse these cells and battery may be saved. Some have thought that sulfation may have occurred where lead sulphate crystals have reduced surface area of your battery plates. Perhaps: a flat battery has 2 plates of PbSO4 but it takes time to make lead sulphate crystals that are hard to dissolve. Therefore charging these cells will be fine.
Rational thing to do is to replace battery, but if you have 2 cars and are interested in spending some time you might like to jump start car and go for a drive - perhaps to a shop to buy another battery just-in-case?
You alternator and regulator will have no problem recharging your battery - they run your car headlights at night with are typically 5A each, and a alternator can produce at least 70A (I think mine is 100A).