### What this PR does / why we need it?
fix(mtp): resolve MTP core bugs and enhance eager mode test cases
1. Resolved critical issues in eager mode MTP core execution logic;
2. Fixed functional bugs in the _update_states_after_model_execute
function;
3. Updated and released test_mtp_qwen3_next.py to validate eager mode
acceptance rate.
### Does this PR introduce _any_ user-facing change?
None
### How was this patch tested?
- vLLM version: v0.15.0
- vLLM main: https://github.com/vllm-project/vllm/commit/v0.15.0
Signed-off-by: Bowen-Leee <caoshankuangren@gmail.com>
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