Number of leaves for lightgbm is smaller than categories in one feature
There are different ways to include categorical features, and in many of them a single leaf can combine multiple categories:


With the label, target, or frequency encoding the categorical feature is effectively replaced by a numeric one, so a leaf can include multiple original categories naturally. Conversely, any numeric feature can be thought of as an ordinal categorical feature with an infinite number of possible values.
With the hash or binary encoding a single bit is activated for different categories, grouping them together.
LightGBM also supports categorical features natively. If they are marked in the configuration, LightGBM will consider various ways to partition all the categories of a given feature into two subsets.
If the one-hot encoding is used, LightGBM can choose to combine multiple categories via the Exclusive Feature Bundling (EFB) algorithm. It is discussed in a related question.


Finally, it is also possible that only a few out of these 1000+ categories are really important (in reality or only seemingly due to overfitting).