This is some high quality pedantry; and I’m here for it.

I agree with your classification but reading nearly any recipe will contradict us

But a tomato isn’t even an actual fruit…

“Actual” refers to the ordinary “plain English” meaning. Under the “plain English” definition, i.e. non-technical, non-domain-specific, a tomato is a vegetable.

It’s a botanical fruit, but an actual vegetable.