This post, if I can manage the links, will show how I first heard Betty Carter in live performance,
and provide some perspective.

That previous post, the link was a studio recording from roughly 1960, and Ms. Carter was in robust good health singing there.

Contrast this with a studio recording from about the same time.
Here the artist is the singer professionally known as Dinah Washington.
She was not all that much older than Betty Carter,
an age difference of less than ten years.
When Ms. Washington recorded this song, she only had a short time left to live,
and already her voice was, let's say, no longer what it had been when she was young.
You will note, listening to Ms. Washington's delivery, that she kind of speaks on pitch through the song, and it's an authoritative performance, knowing exactly how far she can push her voice, and pushing it no farther. Tremendous emphasis on diction, lyrics, the words, in this song.

The link after that is the same song, sung by Betty Carter. Why this choice?
Because, "I Was Telling Him About You" was the first song I ever heard Betty Carter sing live, the opening song of her set at that club in downtown Boston, wasn't it called the Jazz Workshop?
The second link in this post, if it works, is unpleasant in that it seems to be a video of a broadcast of a documentary --
that might explain the truly wretched quality of the sound.
But it is Betty Carter in performance, singing the first song I heard her sing, in much the same way that I heard her sing it years ago.

I don't know the year/date of this performance or documentary. But obviously,
Betty Carter is older, with the pros and cons that gives a professional singer.
Telling to compare this link with her singing "Don't Weep For The Lady."

Dinah Washington, studio recording, 1961

documentary, live performance, Betty Carter