The point is, my battery's voltage drop Is higher even with less current and bigger capacity.
I never got the battery below 70% of its capacity. How am I using it aggressively?
This is the only battery you have?
The 10.8v is the voltage with the load on. Not a resting voltage.
10.8V under load might be aggressive. What discharge rate? As discharge rate increases, the available capacity decreases with lead acid. With a 20 hour rate, the capacity is 200Ah. 10 hour rate is 168Ah, 5 hour rate is 140Ah. What this means is just because a battery is rated at 200Ah, if the discharge rate is at the 5 hour rate, then it is rated at 140Ah.
You really should invest in a shunt and only discharge to 50%. You can use resting voltage but that means you need to cut the loads. 12.2V is 50% discharge.
My inverter has a built in charge controller. I charge it with 30 amps of current. 14.6 bulk and 13.5 float.
What are you using for absorption charge? You need to hold 14.6V for some time as charging amps drop.
Your charge rate at 30A is well above the spec sheet bulk charge of 20A and absorption at 10A. High charge rates will cause excessive heat damaging both the plates and possibly electrolyte if battery is sealed and water can not be added. While you might think 30A is fine, it is higher than manufacturer charge rate plus high charge C rates will affect absorption charge and battery capacity.
I'm sure it is full because the voltage is around 12.8v when the sun goes down. That may not be enough but I'm quite new to this and maybe you can tell me if I'm wrong.
Using solar to charge any lead acid battery can be very tricky as absorption charge may not be completed before discharging occurs. Over time, this will lead to excessive sulfation of the plates resulting in lower battery capacity and lower battery lifespan.
I always recommend a split bank/battery system with lead acid on solar where one half of a bank is fully charged thru absorption charge while the other battery is used for loads. Once the absorption charge is completed, then switch loads to the fully charged half of the battery bank and begin charging the other half. This ensures full absorption charge is reached on a regular basis so short term sulfation is reversed before it causes reduced battery capacity and lifespan. If full absorption charge can not be completed in a day before the sun goes down, then you will probably need to add more battery bank capacity in order to power loads off the battery with the loads overnight. Using the battery before absorption completes can result in hard sulfation and the result is reduced battery capacity and lifespan.
I applied a 10 amp load for 3:15 hours and the voltage dropped gradually to 11.1v. Now it has been resting for 3 hours and I am measuring 12v
Then it is discharged more than 50% as 12.2V would be 50% charge.
Looking at the spec sheet, a 10A load would be 120W and duration should be about 15 hours. (go look at Constant Power Discharge Performance chart).
That is if discharge started at 100% SOC.
Buy a shunt. Fully charge the battery. Ensure battery is at 27°C for 24 hours. Apply a 10A load which is the C20 rate. Run discharge to 10.5V under load. It should run 20 hours. Basically C rate is computed by Ah rating divided by 20 (hours) = discharge rate
You will find lead acid will require a learning curve on your part. It may also be the damage done to your battery is irreversible. Chalk that up to an educational experience. If you want to use lead acid, be prepared to educate yourself on the do's and dont's.