Step-daughter's bio mom refuses to meet her half sister (my bio-daughter)

So I ( 29f) have a 2 year old daughter with my partner (41m), and he has a 10 year old from his previous marriage with 50/50 custody. I'll give you a brief timeline to lay the scene:

-Met partner, fell in love, 3 months in got first angry email from lawyers saying bio-mom had complaints about me. (SD 7 years old at this time)

-Her complaints were dismissed and we went on with life

-8 months into relationship I became pregnant, we chose to keep her 💜

(Partner and bio-mom have custody agreement that SD is not to meet a new partner until 1 year into the relationship

-2 months into pregnancy, roughly 10 months into relationship, partner asks bio mom to meet SD early because we'll have to share the pregnancy with her soon. Bio mom objects harshly saying I'm satanic and makes us wait till 1 year. We do, respectfully.

-3.5 months pregnant, I meet SD, 1 month later partner moves me in to prepare for baby. SD was THRILLED to learn about the baby, mind you.

-I've been living with SD ever since, and we moved into our family home around 1 month after my daughter was born.

-Bio-mom has angrily refused to meet me our entire relationship, even despite living with and taking care of HER daughter in a shared family home for almost 2 years. She formally met me end of last summer and hasn't had any interest in connecting again. She only has briefly seen my daughter in passing; my daughter has no clue who her big sister's mom is essentially. SD has requested for her mother to join party's at our home, or bring her baby sister to her mom's events, but bio-mom has very clearly put up a firm wall and does not have an interest in interacting with us.

So I'm looking for insight as to how I would handle this in the future when my daughter becomes aware that SD has a mother that has zero interest in meeting her half sister. Which, has been incredibly hurtful to SD, hence trying to connect us all together in spite of her mother's adversion to SD's new blended family. CLEARLY there is underlying mental illness, and I'm not here to debate that aspect, but I'm looking for insight from other half siblings/stepparents/blended family parents:

1.) how a toxic bio mom has affected them and how they navigate their half-sibling dynamic

2.) how to communicate this to my own daughter when she starts asking questions (naturally)

3.) how to kindly and lovingly explain to 10 y/o SD why we can't include her mother or half sister because she KEEPS asking and it's becoming increasingly more awkward with bio-mom being adamantly avoidant