If Baumol was solely the reason for increased prices, I expect the increase to be more in line with the increase in prices for hiring tradespeople or other professional services.
FWIW Alex Tabarrok (economist) wrote a small book analyzing this and came away with the conclusion that it's mostly Baumol; if you're interested in a deeper dive:
theptip|2 years ago
https://www.lesswrong.com/posts/FCMfToFnRXhsfpfQB/book-revie...