So first as other commenter has said both hot and cold water come from the single pipe entering the house so pressure of both are the same.
Second if you have 2 pipes with different pressure joining up to a common point e.g. a tap, pressure don’t add up, instead water with higher pressure get pushed to low pressure region. In your example with both handles fully open, the higher pressure pipe will not only push water out of the tap, but also push water backwards into the lower pressure pipe.
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