feat: automate build check and auto-push after merge and format steps

Author: oleander

Justfile

@@ -36,4 +36,4 @@ pr PR_NUMBER CMD:
 
 # Sync a specific PR with origin/main
 sync-pr PR_NUM:
-    just pr {{PR_NUM}} "git merge origin/main --no-edit && cargo fmt --check"
+    just pr {{PR_NUM}} "git merge origin/main --no-edit && cargo fmt --check && cargo check && git push origin HEAD"