Bella Swan's character could be developed by having her explore different aspects of herself. In the context of Greek gods, she might discover a more passionate side of herself, like the passion associated with the Greek concept of eros. This could make her more confident and change her relationships. She could also be developed through her experiences with the Greek gods' powers. If she gets a taste of Athena's wisdom, she could use it to solve problems in Forks that she couldn't before. This would make her a more respected and important figure, not just among the Twilight characters but also among the Greek gods she encounters.
To develop Bella in this fanfiction, she could be given a mentor. Maybe an old witch who has been watching over her. With the mentor's help, she can learn about the history of doppelgangers in the witch world and how to control her powers. She can also struggle with the morality of using her powers, like whether she should use them to get revenge on those who have wronged her in the past.
Maybe Bella is a reincarnation of an ancient figure related to Salazar. And Salazar has been searching for her through the ages. Their meeting could trigger a series of events to save the world from an ancient evil.
In some fanfictions, Bella's character might become more confident. As an immortal, she no longer has the same fears of mortality. For example, she could be more fearless in facing dangerous situations.
Yes, there are some out there. You can start by looking on popular fanfiction websites like Archive of Our Own or Fanfiction.net. Just search for 'bella swan and salazar the greek god' and you'll likely find a variety of stories with different takes on their relationship and adventures.
One way the story could be developed is by having Bella be a secret Mikaelson fan in the Twilight universe. Maybe she discovers a hidden book about the Mikaelsons in the Forks library. This could lead to her having strange dreams about them and it might even influence her relationship with Edward. For example, she could start comparing Edward's vampire nature to that of the Mikaelsons.
She might become more assertive. As the daughter of Ares, she would inherit some of his war - like traits. So, instead of being the somewhat passive Bella in the original story, she could be more proactive in making decisions and taking action. For example, she may no longer wait for others to protect her but instead take the lead in dangerous situations.
She might become more protective. As Silas's sister, she would have a natural inclination to safeguard him, which could make her more assertive.
She might be portrayed as a villain by showing her being manipulative. For example, she could use her relationship with other characters to get what she wants, like using Edward's love for her to control his actions or decisions.
Well, in some fanfictions, she might be depicted as the devil through her actions. Maybe she's shown as being manipulative, using her charm to get what she wants from others, much like how the devil is often portrayed as a tempter in traditional stories.
In the fanfiction, Bella Swan as a fallen archangel may be seen as a more rebellious character. Her fall from grace could be seen as an act of defiance against the rules of the celestial realm. This new aspect of her character could lead to a whole new set of adventures and challenges, different from the love - triangle - centered plot of the original 'Twilight' series. She might be more focused on finding her place in the new world she has entered rather than just on her relationships with Edward and Jacob.