Battery at rest volatege 12.09 V

No, the charging itself won’t damage anything unless you hook the charger up backwards. But the fact the battery will need to be charged frequently means the battery’s lifespan will be shortened. But it may be a goner already.

What kind of volt meter are you using?

Here is the test I would perform:. Disconnect the negative cable. Charge up the battery. After the battery is charged, take a reading with your voltmeter. Wait three or four hours. Take another reading. If the voltage drops, you have a bad battery. You have eliminated a parasitic draw in the car by disconnecting the negative battery cable.
I got a bad battery that would barely crank the engine after the car sat overnight. I disconnected the negative cable and charged it up. I measure the voltage and it was 12 8. I measured the voltage three hours later and it was down to 10.5. I took the battery back to the chain where I bought it. After a big argument where I was told the problem had to be the car, I grabbed the tester and showed the clerk the battery was bad. I was then told that they didn’t have the battery I bought in stock and I would have to buy a more expensive battery. I then asked for my money back. I was told that my exchange battery had already been sent to recycling. I really lost it. The manager got involved. I demanded a refund and any old exchange battery. I finally got my way and bought a new battery at a different store. A few months later, the chain store where I bought the first battery closed nation wide. I felt bad, because I had done a lot of business with this store.