How does xgboost work with linear booster?
Refer to the authors' paper on xgboost here - XGBoost: A Scalable Tree Boosting System.

Equation 3 on page 2 mentions that in each step all the predictors are used to greedily fit the next additive tree.
However, since column sub-sampling is also employed to prevent over-fitting, not all features may actually be used for each step, see section 2.3 of the same paper.

Hence, the specific answer to your query is that the algorithm uses all features to fit the residual.