fix(e2e): improve dind-sidecar probe configuration for reliability

Add startupProbe with failureThreshold of 30 to allow more time for Docker
daemon initialization. Change readinessProbe to use 'docker info' command
which verifies the daemon is actually ready to accept commands.

This is a cherry-pick of the probe changes from tektoncd#9242 on main.

Author: vdemeester

examples/v1/taskruns/dind-sidecar.yaml

@@ -59,11 +59,19 @@ spec:
       - mountPath: /certs/client
         name: dind-certs
       # Wait for the dind daemon to generate the certs it will share with the
-      # client.
-      readinessProbe:
+      # client. StartupProbe handles slow Docker daemon initialization.
+      startupProbe:
         periodSeconds: 1
+        failureThreshold: 30  # Allow up to 30 seconds for Docker daemon to start
         exec:
           command: ['ls', '/certs/client/ca.pem']
+      # ReadinessProbe verifies Docker daemon is actually ready to accept commands.
+      # Note: With k8s native sidecar support, startupProbe is honored but
+      # readinessProbe may not be.
+      readinessProbe:
+        periodSeconds: 2
+        exec:
+          command: ['docker', 'info']
 
     volumes:
     - name: dind-certs