Is it a self priming pump? If not you might have to go through some sort of priming procedure. Although my guess is the pump isn’t, or at least wasn’t the issue.

I would think even with a vent clog you would get some pressure at first and then it would drop off. And different faucets having different pressure indicates to me it’s probably not the pump or vent.

I suspect the faucets inlets are clogged. To check the inlets of the faucet lines turn off water and remove the lines between the wall valve and where they connect to the faucet. There are usually screens that can clog up and kill the flow.