I would suggest you first check the pump filter screen which should be easy to see/locate. If that screen gets clogged, water flow is impaired.
Since you have good flow from city water, the issues seems to be with the pump and/or accumulator, as you suspect, but the easiest one to address is the filter screen on the pump.
The accumulator is typically located close to the outlet port of the pump, so begin your search from there.
Larry, Eileen, and Finley
2004 Alpine 36FDDS
Third motor home, first Alpine, no need for another.