The melodies of "Johnny Fill Up the Bowl" and "When Johnny Comes Marching Home Again" are essentially identical. The evidence is that "JFUTB" iwas in print a few months earlier.

"Ye Banks and Braes of Bonnie Doone" is the name of a song by Robert Burns. Its tune is entirely different.

The two Johnny songs were so popular during the Civil War that there would have been no reason not to adopt the melody to "The Three Crows" at that time, particularly if all a singer had was a printed copy of the words.

It's possible that the Johnny melodies originally belonged to "The Three Crows," but there's no direct evidence of this.

There appears to be no record of "The Three Ravens" between 1611 and the 1820s. The ravens became "crows" later than that - if the sparse records can be trusted.

A big "if."