You can't alter the water level in a toilet bowl. That depends on the design of the ceramic bends and soil pipe connection in the toilet.
You might be able to alter the flush volume for small and big flushes. But the water left in the bowl will remain the same.
How to depends on identifying the make of the flush valve for the instruction leaflet. That one will undo on a bayonet fitting for removal and examination (close fill valve stop tap first).
As above, gravity determines the amount of water left in the pan after you flush
Water, irrespective of the volume, will enter the pan, and leave because of curves/gravity.
I too suspect that you are asking how to increase the volume of water that clears the pan. I am not a plumber. I don't recognise the mechanism that you have though, and will defer to the pros. Best of luck
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