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Intrepid Reporter overlapping with Spirited Young Lady or Plucky Girl depending on the details; may be Plucky Office Girl if the confidence is a facade to cover her frustration with a glass ceiling that has her assigned to cover Yet Another Baby Panda rather than the hard-hitting expose she wants to pursue.
The old-timey fast-talking part is not exclusive to this type of woman; the snappy mid-Atlantic accent was just the norm in films made during old Hollywood.
Paige and Max are specifically riffing on Woman of the Year and His Girl Friday, which happen to be films about love interests who work at a paper, so ^ might be the direction you are looking for.
I asked this question a while ago too if I remember.
I think perhaps there might need to be a specific page for the reporter type of trope? It does surface in a number of things I've seen that I have no doubt is His Girl Friday influenced.
http://sophomorecritic.blogspot.com

Is there a trope for the stock character of a female journalist having fast exchanges with other people in the office, being portrayed as tough, clever and competitive? Usually in stories set before the 1960s, where there would be a single woman in the bullpen and she had to work hard to compete with the boys
I can think of Paige Sinclair from BoJack Horseman as a parody of that type of character.