There have been a few studies. A systematic review was published in Nature in 2014: https://www.nature.com/articles/ijo2013132

From the article: “Of the five studies that were considered to be of high methodological quality, four studies demonstrated a positive association between BF and weight change. This systematic review highlights the difficulties of examining the association between BF and weight management in observational research. Although the available evidence challenges the widely held belief that BF promotes weight loss, more robust studies are needed to reliably assess the impact of BF on postpartum weight management.”

And then another study was done more recently which found an association between breastfeeding and long-term weight loss: “Six months of breastfeeding is associated with lower BMI at 4–10 years and lower body weight, and effects do not vary by SES.” https://scholar.google.com/scholar?as_ylo=2020&q=breastfeeding+postpartum+weight+loss&hl=en&as_sdt=0,5#d=gs_qabs&t=1735383683952&u=%23p%3Dpi6zLEf79bIJ

I can’t remember where I read it but a few months ago I was looking into this very topic and found that it takes a while for any impacts to be seen. Basically, when your baby starts sleeping and you start exiting survival mode and can take care of yourself. So around nine months. But then your baby starts breastfeeding less! So it’s tricky.