I get why it has an Electric typing, but the origins don't explain the Poison-Type being added.
Toxtricity is likely based on the Dyeing dart frog, like you can see in its gigantamax form with its color morphs, a specific characteristic for those frogs. These color morphs in Dyeing dart frogs are usually consistent of yellow and blue. Both the colors that differ from the two Toxtricity forms. Although its Gigantamax form actually combines these colors. And its Gigantamax's basis is likely based on the dyeing dart frog because of the color morphs in these extremely specific colors. Now we got that out of the way, these frogs are poisonous. Which gives you a clear reason for the poison type.
Though also like HeartGoldFan said, it's also a slight pun on 'toxic' being mean.
Just look at his name I mean it starts with TOXIC so presumably it's a poison type and that's what the people who made the Pokemon wanted it to be.
Well,since Band Players are usually/typically seen as "Rude and Toxic"(Toxic in the way that you are mean),the Poison type works fine.But the dark type would have suited it better to be honest.
I am not sure but it could be the g max form entry stating Out of control after its own poison penetrated its brain, it tears across the land in a rampage, contaminating the earth with toxic sweat.
or it could be the fact it has toxic in its name, otherwise I am not sure