[BugFix] Fix the issue of incorrect generated tokens

[amy-why-3459]

PLEASE FILL IN THE PR DESCRIPTION HERE.

Purpose

Fix #4459

Test Plan

vLLM Version: v0.23.0

vLLM-Omni Commit: c58a02c

vllm bench serve \
    --omni \
  --dataset-name random \
  --port 28889 \
  --max-concurrency 1 \
  --model /data/why/Qwen3-Omni-30B-A3B-Instruct \
  --endpoint /v1/chat/completions \
  --backend openai-chat-omni \
  --num-prompts 1 \
  --random-input-len 2500 \
  --ignore-eos \
  --percentile-metrics ttft,tpot,itl,e2el,audio_ttfp,audio_rtf \
  --random-output-len 900 \
  --extra_body '{"modalities": ["text"]}'

Test Result

============ Serving Benchmark Result ============
Successful requests:                     1         
Failed requests:                         0         
Maximum request concurrency:             1         
Benchmark duration (s):                  4.32      
Request throughput (req/s):              0.23      
Peak concurrent requests:                1.00      
----------------End-to-end Latency----------------
Mean E2EL (ms):                          4318.05   
Median E2EL (ms):                        4318.05   
P99 E2EL (ms):                           4318.05   
================== Text Result ===================
Total input tokens:                      2508      
Total generated tokens:                  900       
Output token throughput (tok/s):         208.40    
Peak output token throughput (tok/s):    230.00    
Peak concurrent requests:                1.00      
Total Token throughput (tok/s):          789.14    
---------------Time to First Token----------------
Mean TTFT (ms):                          410.83    
Median TTFT (ms):                        410.83    
P99 TTFT (ms):                           410.83    
-----Time per Output Token (excl. 1st token)------
Mean TPOT (ms):                          4.35      
Median TPOT (ms):                        4.35      
P99 TPOT (ms):                           4.35      
---------------Inter-token Latency----------------
Mean ITL (ms):                           4.35      
Median ITL (ms):                         3.26      
P99 ITL (ms):                            7.54      
==================================================

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[hsliuustc0106]

Fix looks correct. Using continuous_usage_stats to resolve token deltas per SSE chunk and expanding ITL accordingly properly accounts for bundled tokens.

[Gaohan123]

LGTM. Thanks