Electric motor running (near the fuel tank area) every night.

Yes, you figured out correctly it's the evap leak test.

From the description in the repair manual, the leak detection pump is running all through parts B, C, D, and E of the test, so it looks like seven minutes and ten seconds plus however long part C runs. Part C could take up to 15 minutes, so it seems like the longest time you could hear the pump run would be twenty-two minutes and ten seconds worst case.

EPA probably does require the car to test itself for evap leaks regularly. I don't think the car's ECM operates a time-of-day clock, much less a calendar, but just does simple checks like "has the car been off for five hours" and "how many hours has it been since I did this last?"

 

Probably all plugins make these motor sounds. Our volt & Pacifica plugin both occasionally have electric pump sounds going for a few minutes.
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Doesn't even have to be a plugin. The test being run is on the system that captures vapor emissions from a tank of gasoline. Lots of cars have tanks of gasoline.

 

The capacity of the 12 volt battery and the way the evap self test works are choices made by the same engineers, and every Prius has been testing its evap system that way since 2010....

 

You could always buy a more powerful aux battery - in lieu of the oem.
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I don't think the system tests every night- it should only trigger on days you've driven. Theoretically, your drive time will have replenished the electricity used during the prior test. The 12v battery maintenance system in a Prius is pretty smart, but it can still be foiled by not enough driving.

Even the small Prius battery has successfully managed this times millions of Priuseses for over two decades now.

Timed evap checks have increasingly been a thing in gas-burning cars since the late 90s and are now ubiquitous.

 

A person could conceivably put a logging ammeter inline with the leak detection pump, and find out just how many amp-hours or fraction thereof to chalk up to that seven-to-twenty-minute test happening one time five hours after shutdown, and see whether that is large or small in comparison to the other 24✕7 loads accumulating all the while the car is off.

 

I recall it was much less, 20 seconds at most. Could be the test is longer, but more-or-less silent??

 

See post #2; the pump runs through stages B, C, D, and E of the test.

 

You people ought to dig into some of our own old posts. It's like a walk down memory lane.

The latest generations of Prius are not the 1st to wring their hands over the sound of an electric pump running ...

evaporative leak check: how often, how long, drain on 12 volt? | PriusChat

Sound familiar?
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If the gen 3 manual is to be believed, it might even be at least seven minutes and ten seconds.

And it sounds like a little bitty vacuum pump running. Which it is.