Introducing a new chihuahua puppy to my aggressive cat

I’m getting a chihuahua puppy soon and I have an older cat who’s always been pretty aggressive. Someone I trust told me the best way to introduce them is to just let them meet normally and not make a big deal out of it.

The plan is to bring the puppy home and let him explore the house while the cat is around, since the cat already “owns” the space. I was told it’s better not to use gates or keep them separated too much because that can make the cat more defensive, and that the puppy will learn boundaries if the cat corrects him.

Is it better if I leave while I let them interact so they don't get too stressed out? Is there anything else I should do, or am I overthinking it?

Thanks!