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The Composer was inspired by various pieces, including "Invitation to the Dance" by Carl Maria von Weber, because that's what I was listening to when I created him, but I'm calling his official theme song "Lethal Symphonies" from Doctor Strange in the Multiverse of Madness.
In a similar vein, Steampunk Dwarf's theme is "Underground City" by Derek and Brandon Fletcher:
Zebulon Crane's theme is "Hell's Comin' With Me" by Poor Man's Poison. Listen past the opening minute, which acts like an overture before the song really kicks in. Then you'll hear some righteous gothic bluegrass.
Lefty McWright dances a jig to "Sea Front" from the ReBoot soundtrack: