Rebirth BoP tried to show that she could be both but it didn't seem to stick well. Between being Oracle and Batgirl I feel like DC has to commit one way or another.
And then you have the other issue where there are fans of Babs as Batgirl and fans of Babs as Oracle and they seem to have two vastly different expectations of the character.
But most of her main character focus and development happened in Batfamily titles.
But there's only so much the visuals can carry something without the proper stories and meaningful character development to make it matter and get people invested. What separates the Bronze Age and the animated depictions of Babs from Burnside is less flashiness and trendiness in favor of a relatively more straightforward an serious character. There is far more to Barbara Gordon than the '66 show. More Year One than Burnside.
I would say that intelligence and deductive skills were on full display as Oracle.
Oracle did more than just be an information broker though. It's belittling what she was doing by saying it was just a "part time gig" or could be reduced as such.