What's the best way to predict weekly selling data?
There is an ongoing competition on Kaggle right now which is about sales prediction.
https://www.kaggle.com/c/m5-forecasting-accuracy/notebooks

The user kyakovlev have created a series of notebooks where he creates features and creates an lgbm model:

https://www.kaggle.com/kyakovlev/m5-three-shades-of-dark-darker-magic

The notebook linked is the last in the series.
I've had success in applying a very similar strategy on a real-world project for a client.

You probably want to engineer more features and add more lagging variables.

The prophet model could possibly be a problem if the patterns in the data aren't clear. I have had examples where it is completely of. This could be due to the trend. The Prophet model also easily overfit on holidays due to the lack of data. This is due to the nature of the model.
You should definitely inspect what the model is learning.

Models such as XGBoost or LightGBM are great for this type of problem!