Several Communists were charged with treason in 1949 and convicted in 1950, when there was no shooting war going on. The Rosenbergs were convicted of treason in passing atomic bomb secrets to the USSR during World War II, when we were actually ALLIED with the USSR at the time of the deed.
Nope, the Rosenbergs were convicted of espionage. The judge and jury were more willing to impose the death penalty because we happened to be in the Korean War by the time the trial happened, but that of course did not make them liable for a treason charge for what they did in 1944-5.
If you look, I don't believe you'll find a single case of Communists being convicted of treason at that time.
The constitutional provision may not be clear, but the case law is quite clear. The U.S. needs to be at war for a treason charge to lie.