How to cope with boredom whilst cycle touring?
As I may have given away in the comments, I'm not a fan of sensory deprivation when you're as vulnerable as you are when you're on a bike. I don't think there are many scenarios where not being able to hear as good as you possibly can is safe on a bike — but you may not agree and safety really isn't the point of this answer.

My belief is that when you listen to music, you are isolating yourself. Same applies to an audiobook or a podcast. You may as well go the whole hog and watch a movie while cycling on a turbo trainer. The moment you ride with music, the music has become your concentration. You're only going to enjoy the ride as much as you enjoy the music.

Throw the music away and engage with your scenery. Listen to birds, weave potholes, count squirrels... Whatever you do, just enjoy the majesty, the unimaginable effort that went into creating what you're cycling past.

If you can't do that (and can't swap squirrels for the homeless, potholes for bullets — I have no idea what your area is like!) change your route so you're going somewhere that does interest you. Otherwise, as I said before, you might as well be on a trainer doing something that does entertain you.