Aza's father dying impacts her anxiety largely because it removes the person who would best understand it from her life and family.
Aza's anxiety and OCD are ongoing problems throughout her life. There's no indication in the text that they were instigated or made worse when her father passed away. However, it's likely that they did contribute somewhat, despite the lack of in-text evidence. Losing a parent is never easy; for Aza, it happened when she was very young and took away someone that she cared for a great deal. It probably impacted her sense of security which could easily heighten a person's anxiety. She also saw him fall in the yard as he had his heart attack.
However, the book makes it clear that her father dying took from Aza the person who would have best understand her anxiety and OCD. Her mother says:
He would've understood you, that's for sure. He got your whys in a way I never could. But he was such a worrier, and you might have found that exhausting. I know I did, sometimes.
Even when she was a child, her father understood her better than her mother. So his death made her even more isolated within her family. It's safe to say that this also had an impact on her anxiety and OCD.
Aza does seem to use her father's old phone as a touchstone to help reduce her anxiety, though. She likes to use it to swipe through pictures he kept on it. Unfortunately, it's broken in a car accident near the end of the book.