Does it go flat as fast as it charges?
All cells have some self discharge as the diffuse back. Solid state cells should be super low because there is no liquids to dissolve into.
As for flat as in does the rate flatten out yes all cells solid or not flatten out as the ions pack more and more into the anode that is electrochemical. They show 4.5 min to 80% and 7 to 100%
You normally stop at 80% so you don’t cause unnecessary stress on your anode. Sodium cells can take DOD all the way to zero something li cannot do well. So unlike a lithium cell currently where your operating window is 80-20% sodium based cells do 80-0 you get 20% more window and if you are willing to give up some cycle lifetime you can do 100-0..with 50000+ cycle lifes for Na based cells you could cut that in half and still beat the pants off LFP at 10000 cycles or NMC at 3000 both current state of the art. Your smartphone uses a NMC cell, laptops too.
Sorry all cells have some self discharge as the ions diffuse back into the electrolyte. 0.5-3% or so per month is common for NMC and LFP chemistry, sodium ion liquid cells 1-5% per month. Solids should be close to zero.there is no where for the ion to go.