“Our findings suggest that people can improve their mental health by raising or maintaining high levels of tenacity, resilience and optimism,” she said. “Aspiring toward personal and career goals can make people feel like their lives have meaning. On the other hand, disengaging from striving toward those aims or having a cynical attitude can have high mental health costs.”

No they don't. Your findings suggest that people who have more perseverance have reduced risk of depression and anxiety later in life. Additional research would be needed to prove that "we can increase perseverance by aspiring towards goals", and that "increasing perseverance reduces that individuals risk of anxiety and depression". And I would be very surprised if both of these are true.