We researched the name heavily as part of registering our trademark. There are hundreds of hardware/software/internet products and services that use the word "muse" in their name somewhere--and that's true for almost any other single english word or even combination of words.
The practical reality of naming things online in this age is that you try to avoid obvious collisions e.g. don't name your photo editing app Photochop, don't name your computer company Newton's Apple. But there's not a lot of risk of customer confusion between different domains like music sequencer vs thinking workspace.
Simply using MUSE by itself with no other words exposes you to trademark litigation, even from FOSS software. It’s the same business category, according to the USPTO, and the existing project simply named “muse” has an automatic first use to the claim. Merely showing prior use by th undermines your trademark application. I dealt with precisely this issue nearly 20 years ago.
Your assurances are not a legal justification and read like “it’s ok” when it’s really not.
What is it in your first sentence? For just “muse”? Or muse something something? As in is the problem that just “muse” is trademarked in each business category. Or that “muse” is trademarked once with some software and so it can never be used again since there’s prior art? Is audio software and a note taking app in the same business category?
https://en.m.wikipedia.org/wiki/MusE