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My question pertains to this circuit:
Not considering conventional current direction, but rather considering actual electron flow: if the negative terminal is connected to the ground, where do the electrons from the other two grounds come from? The three grounds here are not connected to earth ground, so what is exactly happening for this circuit to function? Where do the electrons from the negative terminal actually go?
Not considering conventional current direction, but rather considering actual electron flow:
It won't help you much. They are equal and opposite.
if the negative terminal is connected to the ground, where do the electrons from the other two grounds come from?
All the grounds are connected. It's a shorthand way of showing the points that are connected to some reference point. This may be the actual Earth or some other convenient common in the circuit.
The three grounds here are not connected to earth ground, so what is exactly happening for this circuit to function?
The symbol they've chosen was originally designed to represent the plates buried underground for an "earth" connection. It still does but is also used (confusingly in my opinion) for other systems such as auto chassis which provides the common negative conductor for all the vehicle electrics.
Where do the electrons from the negative terminal actually go?
Stop worrying about electrons. Just think of current. All the earth points are connected together so current flows as required to or from the battery.
I have written more on the topic in Ground, earth and chassis explained and this may be of help.
All three are connected together. You can just remove the ground symbols and draw a wire between them if that is easier to grasp.
In an actual circuit you would have what is referred as a "common" ground, creating a loop for energy to flow through.
Although, even without this loop, current flows due to a difference in potential (voltage), so from some battery to a ground reference (potential difference 5V-0V ideally) there is voltage for current to flow.
