All this feels like a flag.
Without reading ahead (and thus without spoiling anything) I am inclined to expect that Minami fails and then feels very guilty towards her senpai, adding that to her own drama of siblings' rivalry.
If it were a rich family where children are trusted with some funds and can hire their own retainers (such as “Tensei Kizoku, Kantei Skill de Nariagaru” recently), then Minami could just offer her senpai a decent private scholarship and persuade her like “you should believe it's not favouritism and I really see you as a good tennis player in the future despite not as prodigious as myself” etc.