I always find fan stories of any kind where Chisato is clingy and/or easily starved for attention a bit ooc.
Still, cute story, and I do hope we'll get another one, as foreshadowed in the ending here.
I see it as Chisato, after realizing she gets to live, deciding what she wants is Takina and not holding back. She's always been a do what she wants kind of girl, and she's become truly honest about it. I think what restraint we did see in the show was the fact that she wanted the people she cared about to be okay without her when she was gone. It's obviously just one way to interpret the character, so if that's not how you see it that's okay.
Out of the bunch from this author, this one is my favorite. Writing and comedy feels true to canon. One tiny moment I loved was Chisato whining about being unwanted and Mika saying "you're wanted here. Do your job"
Here's hoping for a sequel!