Does this rim tape need to be replaced? I replaced my very first tube ever after my tire went flat yesterday. I successfully installing a new tube, inflated it, and left it overnight.

This evening the tire was still fully inflated, but after a little riding the tire rapidly deflated again. The new tube has a large tear right at the valve (and after inspecting the old tube, that is also where the tear is.

Inspecting the wheel shows this is what the valve hole looks like:



Was this the cause of the puncture, and would replacing the rim tape resolve this issue? Or is that normally how it looks?

The issue is I don't have a reference of what this part of the rim tape should look like.
One way to get tears around the valve stem is by not supporting the pump head and stem while you're pumping up the tire with a frame pump (the kind where you are pushing on the stem as you pump up the tire, like in the photo below).

Notice the way the person's left hand is holding the pump and the rim. The idea is to stabilize the head of the pump so that no stress is placed on the valve stem.