There could be many ways to explore female friendships/relationships (apart from family) in Greek mythology, but these myth retellers dont look hard enough or arent imaginative enough like for example:
Physcoa and Hippodamia: Physcoa, a Maenad, and Hippodamia are connected to the Heraia. Hippodamia was the founder and organizer of the sixteen women and their rituals, while Physcoa was one of those sixteen women and helped run the Heraia. Hippodamia probably had never met someone as wild as Physcoa (she learned a lot about the world because of her, given that her father kept her inside like a bird in a cage), yet she trusted her deeply as one of her closest companions. I also wonder what happened to their friendship when the whole Chrysippus situation occurred.
Galanthis and Alcmene: It is said that Galanthis was Alcmenes playmate, which likely means they were childhood friends. She also continued to stay with Alcmene even after her transformation. I headcanon that Galanthis sometimes accompanies Hecate and sometimes stays with Alcmene, she is also a talking weasel. We also have Historis, the daughter of Tiresias, who helps Alcmene give birth in other versions, coincidentally, both Galanthis and Historis are of Theban origin, so I like to imagine that the three of them were childhood friends and were always there for Alcmene.
Amphithea and Pelopia are also very likely friends, given the vase painting where they interact and comfort each other. It makes me happy to think that Pelopia had a friend who cared deeply about her despite her tragic life, so I hope she experienced happy moments even if they were short-lived. They were also both married to their uncles, so maybe they bonded over that.
Then theres Arsinoe and Clytemnestra. Arsinoe was the nurse of Orestes and saved him from his mother, Clytemnestra, by carrying him to Strophius. I imagine that Arsinoe and Clytemnestra were once close friends, and that Clytemnestra trusted her deeply before everything involving Iphigenia happened. Arsinoe initially tries to stay with her, giving her moral support and trying to calm her down, but Clytemnestra is too far gone, she lost her precious daughter, after all, so they are a "we used to be friends" case.
With Periboea and Hesione we dont have much in canon but i like to think Hesione was initially scared of Periboea, thinking that she is a jealous wife and is going to hurt her, only to be confused by Periboea kindness. Periboea, in turn, shares that she was also abused by Telamon and with her privilege as queen, tries to ensure that Hesione has a comfortable life and that she and Teucer are not harmed. This contrasts with the usual depiction of women in Greek mythology being jealous of their husbands illegitimate children. So both Periboea and Hesione have a sense of female solidarity and try to survive their circumstances together while bonding over their fates.
