Zero-inflated independent feature in tree-based models
Basically, for categorical random variable, the decision tree will try all potential splits and select the one that minimizes the mse. For continuous random variable, the decision tree tries to find the split which minimizes the mse. You may see that categorizing the data makes fewer potential choices for the split, and, therefore, is not optimal in accuracy. On the other hand, fewer splits to consider during the training decrease running time.
My answer is as follows.
If the train time permits, I would do option 1. This way, you don't lose any data. Maybe exact value of the feature is a key. It may the point especially if your response is unbalanced. Say, this feature may be a good predictor of your response if positive. For example, radiation level is zero for most of people, small positive values are OK, but large positive values are the key. However, we don't know how large values we should look for.
Option 2 speeds up training time which may be of benefit.
Option 3 creates unnecessary redundancy.