Why is my inverter always in battery charging mode?

You purchased a new inverter and installed it yourself. That is not an issue
if you know all the connections that need to be.
● As you are saying that you needed to fill the battery’s water as they were
drained out I am assuming that you are using old batteries with the new
inverter unit.
● The connection seems fine as by hearing.
● The main problem with your set according to me is that if your batteries
that you are using are old they are consuming more power and easily drain
out with minimum loads also.
● Therefore it is always charging.
● If your batteries are new, in that case ask the person from whom you
purchased them and have a check on them.
● Regulated ups are better than unregulated ups mode.
● When regulated UPS mode, the UPS supplies electricity instantly to the
house and a continuous flow is present.
● When in unregulated mode, the UPS waits for around 2 minutes and then
starts supplying loads.
● Thus keep your inverter always on regulated mode.
● Earlier devices used fuses in order to have a control and damage free unit
in case of overvoltages.
● But now they are equipped with MCB just to provide better safety and ease
of excess.
● Once the fuse was damaged you needed to buy and install a new one but
now just turn up the MCB whenever it trips down.