Tears represent emotion and sensitivity, and are associated with weakness and femininity. Katsumata-san exists as a woman in a patriarchal workforce, and adapts by showing anger, an emotion commonly associated with men rather than women.
However, the tears and sensitivity that the main character cannot fully hold back are also her power; when a person feels their vulnerable emotions and moreover shares those emotions productively with others, they create a community founded on authenticity. When we embrace authentic vulnerability, we access the power and strength of humans who are in alignment with themselves and their values.
I think it makes sense when you read the whole thing as a metaphor.