[PSM Interop] Enable affinity_session_drain_test for cpp (grpc#36064)

Add `gamma.affinity_session_drain_test` to `grpc/core/master/linux/psm-csm` test suite.

Closes grpc#36064

COPYBARA_INTEGRATE_REVIEW=grpc#36064 from sergiitk:psm-interop-ssa-draining a161855
PiperOrigin-RevId: 613738983

tools/internal_ci/linux/psm-csm.sh

@@ -161,6 +161,7 @@ main() {
   test_suites=(
     "gamma.gamma_baseline_test"
     "gamma.affinity_test"
+    "gamma.affinity_session_drain_test"
     "gamma.csm_observability_test"
     "app_net_ssa_test"
   )