[CI] Finally fix drivers update testing (#10777)

First (incomplete) part has been merged in #10759.

Author: aelovikov-intel

.github/workflows/sycl_precommit_linux.yml

@@ -97,6 +97,7 @@ jobs:
       image_options: ${{ matrix.image_options }}
       target_devices: ${{ matrix.target_devices }}
       reset_gpu: ${{ matrix.reset_gpu }}
+      install_drivers: ${{ matrix.install_drivers }}
 
       ref: ${{ github.sha }}
       merge_ref: ''