the robots.txt angle is interesting. legally it's not binding but practically violating it can affect how courts view your conduct (vs. good faith compliance).
for public data that's already freely accessible with no login, the case law is actually more permissive than people think — especially in the US after the hiQ v. LinkedIn ruling. the EU is more restrictive.
the music data use case you mention: scraping metadata (song titles, artist names) is different from scraping audio. metadata is generally considered factual/non-copyrightable. audio is obviously protected.
personally i've built some music tools that aggregate public chord/tab data. the legal gray area is real but the risk profile is different depending on what you're doing with it.