[Doc] Document precheck-pr skill in PR template and contributing guide

Add precheck-pr reference to PULL_REQUEST_TEMPLATE.md BEFORE SUBMITTING
section, and add a new "Pre-Check with Claude Code" subsection to the
contributing guide.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Signed-off-by: hsliu <liuhongsheng4@huawei.com>

.github/PULL_REQUEST_TEMPLATE.md

@@ -18,4 +18,7 @@ PLEASE FILL IN THE PR DESCRIPTION HERE ENSURING ALL CHECKLIST ITEMS (AT THE BOTT
 - [ ] (Optional) Release notes update. If your change is user-facing, please update the release notes draft.
 </details>
 
-**BEFORE SUBMITTING, PLEASE READ <https://github.com/vllm-project/vllm-omni/blob/main/CONTRIBUTING.md>** (anything written below this line will be removed by GitHub Actions)
+**BEFORE SUBMITTING:**
+- Run `/precheck-pr` in Claude Code for a self-check against project conventions — catches dead code, missing benchmarks, and title format issues.
+- Please read <https://github.com/vllm-project/vllm-omni/blob/main/CONTRIBUTING.md>
+(anything written below this line will be removed by GitHub Actions)