baby loves mommy boobs 😂

Kendra
I know that all baby's I'm sure , are attracted to their mothers breast .. for obvious reasons.  And I hear stories all the time about mommy that nurse , their babies messing with the other breast while nursing. Here is my question , do formula fed babies always have that need? Lol. My baby girl is 13 weeks old , formula fed and she is always playing /touching my boobs lol. As soon as I pick her up , her hand immediately goes down my shirt , she sleeps on my chest sometimes and fluffs my boobs like pillows until she is comfy , and just the last couple of days she has started trying to twist my nipple while she's eating or trying to sleep! I don't mind , now when she does it in public I worry because she'll pull my whole shirt down trying to get her hand where she wants it 😂😂😂 I guess I'm wondering , does the poor baby think I'm holding out on her? Should I let her latch on so she knows they are empty? (Im half serious about the questions I just wonder if anyone else's baby does the same ;)  I do feel bad in case she wants to nurse :(
And also wouldn't she be getting over it instead of worse as she gets older ?