There's an interesting give and take between vocal and instrumental jazz, beginning with Armstrong who was both the first great recorded jazz singer per se and the greatest soloist of the earliest period of recorded jazz. Really great horn players listen to singers and often model themselves after vocal stylings. (I've heard classical wind and brass players say the same thing so this isn't limited to jazz.) You can hear this in Lester Young, who admired Billie Holiday and Sinatra; in Miles Davis, who often interpreted songs sung by these same singers. The singers also provide a connection to the songs themselves.
By the same token a singer can model his or her stylings on horn players.
A playlist based on this concept might begin with the following:
Armstrong playing and singing "Body and Soul"
Sinatra and MIles playing their separate versions of Rodgers and Hart's "It Never Entered my Mind."
Sinatra and Lester Young playing their separate versions of "Taking a chance on Love."
Lester Young accompanying Billie Holiday on the collection "A Musical Romance" (various songs)
John Coltrane playing with singer Johnny Hartman on "My One and Only Love."
Vocalese versions of "Moody's Mood for Love." An improvised jazz solo by James Moody on the tune "I'm in the Mood for Love" later set to words.
When swing style pop vocals like those of Tony Bennett became eclipsed by rock music in the mid 1960s, it freed Bennett up to be a jazzier singer. The same happened with Rosemarie Clooney--a pop star in the 1950s but a jazz artist later in life. Interestingly, rock musicians popular in the 1970s like Linda Rondstat and Rod Stewart, Joni Mitchell, also turned to the great songs of the great American songbooks much later in their careers--with varying results, some good, some bad.
Nat Cole began as a jazz pianist. When he began singing that talent eclipsed his piano playing and he became an international pop star. His brother, Freddie Cole, has had an interesting career as a jazz singer, using a Nat King Cole-like voice but a more jazzy, less pop feel. Even Armstrong did pop vocals in his later career that have little to do (seemingly) with his jazz roots: "It's a Wonderful World" and "Hello Dolly."
Vocal music, then, has always been close to the commercial side of jazz, often to the point of not being jazz anymore. To what point the dichotomy between jazz singing and popular music is valid, I don't know. Is Sinatra singing jazz with Count Basie and pop with Nelson Riddle? For me, Sinatra is a jazz artist. He even tried to hire Billy Strayhorn away from Duke at one point...