Uncertainty prediction in Gradient Boosted Tree based Quantile Regression

For an application, I am using a Gradient boosting Tree based quantile regression model (LightGBM, Catboot) to predict the 5th percentile of the target variable. The model predicts point estimates, but I want to attach confidence in which the model predicts quantile value.

I read some of the recent research -

NGBoost (https://stanfordmlgroup.github.io/projects/ngboost/) - Used for Regression tasks

Uncertainty prediction with Gradient Boosting Trees (https://arxiv.org/pdf/2006.10562.pdf) - Also for regression tasks.

Is there a way to attach a confidence(probability) value with the quantile regression estimates made by the model?