Recently I have not done mortice and tenon. Because I have the small and large version of the Festool domino cutters. In my view either or is good.Poplar is one of the most abundant timbers in North America. Google 8/4 poplar lumber. Add your address and see what pops up. I think a 5/4 or 6/4 door inside would be adequate. Door making requires straight lumber. No heart wood. An experienced eye buying or ordering the wood can matter.
I will await the contributions of more learned members of the forum, but that seems like a lot to me. I would have thought .005 would have been a more appropriate goal.
You certainly don't need a feeler guage to see the discrepancy with your straight edge. But how accurate is the straight edge? One thing I have learned from hanging out here is that there is a difference between straight enough for a stair case or rafters and straight enough for joinery.
So if that is an ordinary inexpensive carpenter's square it may not be accurate enough for this task. If that's a precision straight edge. Then yeah that table don't look flat.