Is my battery really fully charged? Should I use the "pulse repair" button of my charger?
I would defenetly look at the multimeter readout. It looks like the battery is dead. When the voltage on 12V battery falls &lt;9V it get's permanently damaged.
You can attempt to charge the battery using bench PSU, with low current at the start, however the capacity will be signifficantly lower forever.
I used to repair those batteries with charging them on bench PSU, adding distilled water, charging, adding few drops of water, discharging, charging, water and so on. But this is probably not worth it.