In this pretend family, Yor is Anya's step-mom even though in a way Loid is like Anya's step-father in adopting Anya. I guess this is why Yor calls Anya as Anya-san? Idk.
Being a 'normal mother' isn't something Yor knows how to do. She lacked social and interpersonal skills. She was shown to be insecure about herself and her abilities, believing she is not good at anything apart from killing or cleaning. At the start of the series, she knew that her family is false and didn't have strong personal ties beforehand**. She considered Anya as her stepchild instead of her biological child. That's why, she acknowledged Anya as Anya-san.
Secondly, she is very polite. Her dialogues are very formal, even when addressing towards Anya. Hence, she keeps the -san honorific. She doesn't change the honorific at the later part of series also.
**Despite all of this, she is a genuinely kind person with a strong maternal instincts. After becoming a family with Loid and Anya, Yor becomes more expressive and opens up to her coworkers, asking for help on being a better wife or cooking. She is protective of her faux family, especially towards Anya whom she has no trouble defending with extreme violence.