Your 1/2" copper is already undersized for the load without adding the shower. Increasing the size of the pipes to the shower to 3/4" will not help you enough to notice.
You need to increase the main supply lines to 3/4" to the bath then branch off with 1/2" to the fixtures.
As a rule of thumb I only run two fixtures on a 1/2" line.
Water pipe sizing





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