The "Sinatra = jazz singer" thing has been going on for 50-60 years (I think there was a rather long article in the old Saturday Review about it in the late 1950s/early 1960s). I've thought about it for far less than that, but have still come to the conclusion that Sinatra was not a "jazz singer". He was simply a superb singer who only sometimes sang "jazz". and overall, I value his ballad singing more than I do his swing singing. But I certainly enjoy them both, immensely. Sometimes.
Jeanne Lee - that's a "jazz singer". Joe Carrol. Betty Carter. Johnny Hartman. People who satrat and end inside a "jazz" esthetuc (and no, I won't try to definte what that is LOL)
In the end, for me, again - singing first, style second. Perry Como AND Jeanne Tyson. Why not?
Singers (usually) have lyrics to deal with and the is a fundamental differentiator in so many ways. Instrumentalists (almost always) don't have to deal with vowels and consonants and stuff like that. Phrasing, yes, shading, yes, tone placement, yes, but vowels and consonants? No, not unless somebody going to get extraordinarily "vocal" about there instrument, in which case, go ahead and sing. Because an instrument can be "vocal", but an instrument cannot speak actual words (although Mingus/Dolphy almost could!).
These days, they "teach" you (the instrumentalist) to keep your throat open at all times to keep a solid/steady air flow going, but hell - there is SO much you can do about tone production with your throat, and singers know how to do this. Instrumentalists can, but generally don't.
The voice is really the most flexible and difficult instrument, imo. Ignore any good singer, regardless of "style", at your own peril!