As you found, each state has their own approach. Massachusetts taxes "Massachusetts sourced income." Yes, they tax both nonresidents working in Massachusetts as well as their residents working in other states. Their caveat for COVID-19 is a credit for out-of-state taxes incurred for Massachusetts residents.
TurboTax will apportion your earnings during the interview as a Nonresident of Massachusetts to Florida if Form W-2 does not withhold Massachusetts tax.
If your W-2 has MA taxes withheld, then you will have to pay Massachusetts tax and cannot exclude it. The Massachusetts state tax could have been credited to your resident state return, but since Florida does not have income tax, there is no offset.
Per Learn about Massachusetts gross income for nonresidents from Mass.gov:
Included in Massachusetts gross income: Massachusetts gross income includes income from sources within Massachusetts.... and later it contradicts itself by saying in Massachusetts.
