I've had oil pumps fail in the past with the bypass sticking open. Swap on a different oil pump. A-series oil pumps are externally mounted and only take a few minutes to change.

Other testing-

Remove the spark plugs to make the engine easy to spin and take the load off the bearings. Take out the oil pressure sender. Spin the engine with the starter motor and see if oil comes out the sender hole. If no oil comes out you have a dead pump.

With the new oil filter you may need to fill it completely full of oil to get the pump to prime. I've never had an issue with priming but you have to cover all the bases.

Don't run the engine (only spin with starter motor) until you know that oil is getting pumped, then put an oil pressure gauge in place of the oil pressure switch to check if you are getting oil pressure.

It will take a long time for oil to show up and be visible through the oil fill cap.