Sounds like water. Install a water filter and new gas. Had the same issue years ago, idles fine, but stumbles on acceleration. The water filter fixed it.
Could even be as simple as a new pump bulb on the fuel line.
Fingers crossed. You can test this by squeezing the bulb with the throttle engaged? If the engine jumps then its not an issue but if nothing occurs then its a fuel line/bulb issue?
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