Are "Many believe" and "supposedly" exact synonyms?

Question

In IELTS exam we have to paraphrase the question in the introduction of the essay. If the question includes the following sentence:

Many believe that listening to classical music confers several advantages on children.

Does it have the same meaning if we replace "Many believe that" with "supposedly" ?

Supposedly, listening to classical music confers several advantages on children.

I guess it would mean exactly the same because according to dictionary, "Supposedly" means:

according to what is generally thought or believed but not known for certain

Answer 1

My take is that they aren't exact synonyms, even if they seem to denote the same thing.

"Many believe that..." is neutral about what follows.

"Supposedly..." seems to put what follows into question right from the start.