I believe the GFCI outlet is a 15A outlet on a 20A circuit, but am not sure.
Coming in later to this one but this sounds like more of an electrical issue than plumbing.
Do you know how many amps the pump is supposed to pull? Do you have an amp meter? If so check how many amps the pump is pulling. Check how many amps the whole circuit is pulling.
(in a perfectly wired world) CFCI’s are “supposed” to be on a dedicated circuit. If not, what other devices are on that circuit? AC unit? If it is dedicate are there any other downstream outlets? Does the CFCI trip any other times?
An ohm meter showing continuity ground to neutral is normal unless you are on a sub panel. If this circuit is on a sub panel and you have continuity, you either have a miswired panel or a faulty ground/neutral, which may not play nicely with the GFCI.
What color is the feed wire to the outlet? White/yellow (in the northeast), yellow romex is (typically) 20 amp, if so you should have a 20 amp GFCI. 20 amp outlets are “generally” identified by and extra vertical ear on the neutral.
Along those lines, does the breaker matchup with the wiring? If it’s yellow Romex it should have a 20 amp breaker.
More along those lines, what type of breaker? If it’s an arc fault or GFCI breaker, that redundancy will (again) not play nice with an additional GFCI downstream.
Like that William guy said: "With all things being equal, the simplest explanation tends to be the right one.”