Is a transition from 1/2" tubing to 1/4" and back causing low pressure?
I would time how long it takes to fill a 1 gallon jug and see if the system is operating within specifications. With a 1/4” line I would not expect a large flow. But no the changing sizes won’t affect the flow as the 1/4” would be the limiter. The size change won’t really help or hurt in this limited length.