Nope. He isn’t. LtCmdr Paul Stamets isn’t an Engineer and he never has been. He’s a Science Officer. He works in Engineering Test Bay Alpha but he isn’t an Engineer himself. Jett Reno is the highest ranking Engineering Officer we ever see on Discovery.

In Season 2, Reno goes into Stamets lab and says “The Chief sent me here” so we know there’s a Chief Engineer and it isn’t Stamets.

That link doesn’t have any information about Stamets after Season 1. I think they’re using ‘chief engineer’ to mean the ‘main engineer we see’ but that’s not even accurate. Then again, Memory Alpha calls the Chief Medical Officer the ‘head nurse’ so fuck knows what’s going on.