Why do features increase R2 but not affect predictions?

Question

I created a machine learning model to predict the daily rate for short term rentals. I have about two thousand rows of csv data about short term rentals with a large amount of features.

However, the only features that impact the predicted daily rate are the # of bedrooms and the property type (condo, house, etc.). This made sense to me at first, until I saw that removing those features from the model decreased the R2. It also seems strange that a property with a pool as an amenity would not charge more. I have tried changing the estimators and some feature engineering to increase the R2 to no avail.

Can someone explain why my model would have lower R2 for features that don't affect the predictions? What other options do I have to increase my accuracy?