Does merely inserting cotton into the vagina by a woman nullify ablution, and does this ruling apply to clothes if they accidentally enter the vagina or the buttocks?

A woman's private parts are divided into an outer vulva and an inner one. Inserting something into the outer vulva does not invalidate ablution (wudu’). However, inserting something into the inner vulva does affect ablution if the inserted object emerges wet. If it emerges dry, there is a difference of opinion, but it is more cautious to perform ablution. Similarly, if something enters the anus, and it emerges wet, it invalidates ablution; otherwise, there is a difference of opinion. Based on this, the entry of clothes into the inner part of the buttocks or anything into the outer vulva does not invalidate ablution.