I assume this is in the context of his alleged pro-Nazi sympathies, which he almost certainly had. It was well-known enough that he was, at the least, sympathetic. The Nazi brass even thought that the Abdication Crisis was an establishment plot to remove him because of those sympathies. Of course, this says more about the Nazis' fundamental misunderstandings of Britain and British constitutional politics than it does about the Abdication Crisis itself; at the time, the establishment was still divided on the extent to which the Nazis even posed a real threat to British interests (the crisis coming before the Anschluss of Austria, Munich, and the Invasion of Czechoslovakia). To think that same establishment would endeavour to take the extreme step of removing a monarch over Nazi sympathies was ludicrous.
However, as far as treason goes, quite simply nothing he is known to have done would constitute it.
His visit to Berghof in 1937, while against the advice of the government, was a visit to a nation that Britain was not at war with (and again, a nation that many in the establishment still considered an acceptable alternative to the spread of Soviet Communism).
In the early war, while there were fears the Duke and Duchess might be captured by the Germans as they fled the Fall of France to Spain and then Portugal, and even kidnapping plans by the Germans, the concern was more about what a return to Britain could do. He might become a rallying point for the anti-war movement, whether he spoke or not; 'champion of the disgruntled' is how George VI put it in his diary [1]. However inconvenient that might be, it is still not treason. Similarly, the couple's conditions for returning to Britain instead of staying in Portugal were inconvenient (and somewhat hilarious, considering the government were agonising over precisely how to avoid bringing them to Britain) but not treasonous. The most suspicious thing the Duke did was request the Germans to guard his residences in France, which they did; odd, but not exactly compelling evidence that he was actively working for them.
When he was posted to the Bahamas as Governor in order to get him out of Europe, German plots continued to surface, a German aristocrat turned monk accused the Duchess of passing secrets, and the Duke gave an interview to Liberty magazine where he proposed that it was time for FDR to step in as peace mediator. A pain that prompted the Americans to put him under surveillance when he visited the States, but not a treasonous pain as far as anyone could tell.
In addition to the lack of concrete evidence, putting a former monarch on trial is a big move. Putting a former monarch on trial for treason is a massive one. Short of joining the Germans and becoming The Duke Haw-Haw of Windsor, it is hard to think of something The Artist Formerly Known as Edward VIII could have done with the resources at his disposal to justify such a huge step. He was certainly not getting within a hundred miles of any sensitive material he could pass on, even if he had wanted to (that the Duchess could have been passing on secrets, as claimed by Father Odo, is even more unlikely).
[1] - Roberts, Andrew, Churchill: Walking with Destiny, (London, 2019) 567