The datasheet of a 555 shows that its pin 2 is the input of a comparator, not an output. The pin 2 input voltage is compared to the voltage set by three resistors inside the 555 that sets its trigger voltage at one-third of the supply voltage of the 555. Pin 6 is shown to be the input of another comparator set to two-thirds of the supply voltage. Your zener diodes leave pins 2 and 6 floating with no set voltage. Because the inputs are floating then the 555 output is erratic.
The label on your tiny lead-acid battery says that its initial charging current is less than 2.1A but does not say if the battery limits this current or if your charging circuit must limit the current.
It looks like R1 (1k ohms) in series with D6 on your circuit charges the battery with a very low current.
You do not understand how to charge a lead-acid battery. It is fully charged only when its voltage reaches a certain voltage and its charging current has dropped to a certain low current.
Go to to learn about it.
Then you should read about battery charging circuits for lead-acid batteries and about comparators.