[CI]Upgrade niglty multi-node-tests max-parallel to 2 (#7035)

### What this PR does / why we need it?

1. Increase nightly multi-node test max-parallel from 1 to 2, and fix
resource conflicts that arise when tests run concurrently.
2. Fix parse-trigger job: Add an if condition so it only runs on
schedule, workflow_dispatch, or PRs labeled nightly-test
3. Adjust nightly schedule: Shift trigger time from 24:00 to 23:45
(UTC+8)

### Does this PR introduce _any_ user-facing change?

### How was this patch tested?

- vLLM version: v0.16.0
- vLLM main:
4034c3d32e

---------

Signed-off-by: hfadzxy <starmoon_zhang@163.com>

tests/e2e/nightly/multi_node/scripts/lws-a2.yaml.jinja2

@@ -1,7 +1,7 @@
 apiVersion: leaderworkerset.x-k8s.io/v1
 kind: LeaderWorkerSet
 metadata:
-  name: vllm
+  name: {{ lws_name | default("vllm") }}
   namespace: vllm-project
 spec:
   replicas: {{ replicas | default(1) }}
@@ -128,7 +128,7 @@ spec:
 apiVersion: v1
 kind: Service
 metadata:
-  name: vllm-leader
+  name: {{ lws_name | default("vllm") }}-leader
   namespace: vllm-project
 spec:
   ports:
@@ -137,6 +137,6 @@ spec:
       protocol: TCP
       targetPort: 8080
   selector:
-    leaderworkerset.sigs.k8s.io/name: vllm
+    leaderworkerset.sigs.k8s.io/name: {{ lws_name | default("vllm") }}
     role: leader
   type: ClusterIP