Wikipedia lists him as a Physicist though, so someone forgot to sneak in a few edits before publishing their article...
Anyway, the ultimate "engineering" Physics Nobel prize remains with Nils Gustaf Dalén, who got it for inventing an automatic valve. But probably really got it for being a good friend that had his face blown up in an accident shortly before the winner was to be announced.
In fairness he did have a PhD in mathematical physics so characterizing him as an engineer instead of a physicist is not quite accurate. That said people in academia routinely downplay the qualifications and abilities of people who work in industry. It’s not hard to imagine colleagues dismissing his work as mere engineering and not real science before he won the Nobel prize. Perhaps calling him an engineer is fair in light of such practices.
I think you've invented quite a backstory about him being marginalised, but consider that when he left Bell labs he got offered a wage 17% short of a US congressman or the top 3% of engineer or "natural scientists" wages. This is not the pay for someone whose work is being dismissed.
My point was that actually he was mainly a physicist that simply started by studying engineering.
Before obtaining his Nobel prizes, he first obtained his PhD in physics (under Eugene Wigner, no less).
That said, Bardeen taught as a professor of electrical engineering and as a professor of physics at the University of Illinois at Urbana–Champaign from 1951-1975, so I think it's fair to call him both.
Fields of study often have very hazy demarcations. Venki Ramakrishnan got a Nobel Prize in Chemistry, something he finds quite amusing because he has never worked on chemistry. He spends a bit of time explaining his background and his amusement in his book, "Gene Machine".
Anyway, the ultimate "engineering" Physics Nobel prize remains with Nils Gustaf Dalén, who got it for inventing an automatic valve. But probably really got it for being a good friend that had his face blown up in an accident shortly before the winner was to be announced.