I think the pause is because the audio runs on a separate thread than the game logic, so the micro pause is the time it takes to communicate to the audio to continue playing. At least, that is what I gather from this page on syncing gameplay with audio on the latest Godot documentation.
In the jam version of Dreams of Fire, I got around this issue by fading the music. I lowered the volume down to zero when changing, and then in the new scene I would slowly increase the volume back to the default, which worked fairly well at the time.
There might be a way to tell the audio to instantly start playing, but I have no idea what it would be, unfortunately. One way you could maybe get around the issue is by instancing and managing an AudioStreamPlayer node in the global singleton directly, though that will have it's own complexities.
Unfortunately, I really don't know. Hopefully someone who knows more will chime in with a potential solution.