Yes, Edward VIII did support Nazi Germany, but treason is unproven.
The only reason why he was appointed governor of the Bahamas and not locked up in the Tower of London was his status as former king. As governor he was under constant surveillance, to prevent any mischief. (He managed to do that anyway when he went on a holiday to the USA.)
How did he support Germany? As king he wanted to rule more like an absolute monarch than a constitutional one. That seriously clashed with parliament. One of the clashes was about his admiration of Germany, in particular for the Führer. Admiring Germany was not a problem, the royal family came from Germany and most royals (including Edward) spoke it fluently. Admiring Hitler was a different matter. As king he couldn't (and shouldn't) do that. Edward resented that limitation, and went out of his way to show it.
Before the war, but after his abdication, he went on a tour of Germany where he met Hitler. He was received with far more honors than his present status (abdicated king; now duke) warranted. That, on its own, is not treason. Reprehensible, certainly. Even in democracies one does not accept that kind of honors.
During the May campaign, after his abdication, he served as staff officer with the BEF. As such he knew all about the Allied planning. He carelessly told what he knew on a party to Italians diplomats present.
That is the best I could find. He spilt the beans over too much champagne and caviar to the wrong people. Italy was not at war with the allies - yet. Had he been a regular officer, it would have ended his career there and then. He wouldn't have been convicted of treason, rather cashiered for carelessness.
When the BEF retreated to Dunkirk, the duke left his post and traveled in his car with his wife and entourage (driver, personal servants) first to Biarritz and later to Lisbon. They traveled in a couple of cars, with ducal insignia on the duke's car. The duke didn't travel light. With, one might presume, permission of the Germans. Which is rather odd, if not outright suspicious.
Not treasonous, but certainly questionable. A regular officer would definitely be court marshaled for it. It was either AWOL (absent without leave) or desertion. The duke social status protected him.
Churchill had to use pretty strong language to force him back to Britain. Only then he could be send to the Bahamas for his tenure as governor.
If anything, the Netflix series portrays the king more favorable than he actually was. He never publicly apologized for his behavior, not just his betrayal of his country but more in general. Maybe he did apologize in private, but we'll never know that. Given the fact that relations between the queen and the duke were ice cold until his demise, I don't think he privately apologized.
Did he factually commit treason?
No, he didn't.
He was never charged as such. Given his social position and political consequences it was a certainty he would not even be accused of
treason.
Especially high treason is a crime with very specific conditions. For a man as the duke of Windsor it is quite difficult (nearly impossible) to be convicted of it. Even accusing a former monarch of treason has enormous ramifications for that monarchy. That is the main reason why he wasn't charged. On the other hand, look at how his family ostracized him. He lived his life out in near total exile.
After I posted my answer I dug deeper into this question: did he actually commit treason? All I can come up with are unsupported accusations. Unsupported, yes. But strong enough to warrant close investigation and making damn sure he wouldn't get into a position where he could commit it. The duke greatly disliked his forced exile on the Bahamas, but it was the safest and remotest place he could be send to. Governor of Saint Helena or the Falkland Islands would be a bit too obvious.
