Eat play sleep (9weeks old)

Any babies out there having this eat play sleep routine? Im currently fully breastfeeding my baby. My baby ended up with play eat sleep :( tried feeding her after she wake up and then play with her but when after playing with her i can see she like hungry again. Then i will feed her and she will fall asleep while breastfeeding. The best I could do is when i see her falling asleep i will put her down and if she wakes up i wont pick her up so she knows how to drift back to sleep on her own. Anybody experiencing the same issue? And how did yall make sure baby doesnt associate feeding to sleep?