We know that sister is adept at attracting friends. Yes, it is probably natural that OP’s brand-nedw proto-friends were attracted to sister, whom (as you suggest) will know exactly how to respond to draw them to her). My issue is simple: knowing that OP is friendless and in the process of creating a friend group out on her own — a big step for OP, which takes real courage given her anxieties, why on Earth would her sister intrude in that new activity. Whether intentional or accidental, this harmed OP. Even in totally normal circumstances, where one sibling isn’t high anxiety and the other an extrovert, I think it is a good thing for siblings to each have at least one activity which is theirs alone and not shared. That’s how a person, especially an anxious introvert successfully establishes their own identity and friend group. My brother is close in age and we did a ton of things together as children and young adults, but we each had our own unique activities. Looking back, I see that as extremely important. I am the introvert of the family.
What you’ve not addressed is why sister would decide to glom onto OP’s activity.