Update serve chat parsing
Author: SunMarc
Pull request: yes

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# What does this PR do?

This PR updates the support for reasoning and tool calling thanks to @Rocketknight1 nice [response parser](https://github.com/huggingface/transformers/pull/45847).

Now, we rely only on  `build_response_parser` for streaming and `parse_assistant_message` for non streaming path. The new streaming `ResponseParser` takes care of `tool_calls`, `reasoning` and the `content`. Thus we removed `tool_config` or `reasoning_config` as those are defined in the new `response_template`. In order to add support for a new model, one only needs to add the template to `_RESPONSE_TEMPLATE_FALLBACKS` if it is not present in the model's config. 

With this new parser, tool calls are now returned as they stream — each one is emitted the moment its </tool_call> closes, instead of waiting to parse the whole output at the end of generation.

Comments:
Let me know when you'd like a review!

**[For maintainers]** Suggested jobs to run (before merge)

run-slow: gemma4

The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/transformers/pr_46267). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

Can you have a look @LysandreJik ? We can merge this now since @Rocketknight1 merged his PR. Feel free to have a look also @Rocketknight1 ! 

run-slow: cli

[Workflow Run ⚙️](https://github.com/huggingface/transformers/actions/runs/28879725758)

This comment contains `run-slow`, running the specified jobs: 

models: ["cli"]
quantizations: []

run-slow: cli

## CI Results
[Workflow Run ⚙️](https://github.com/huggingface/transformers/actions/runs/28879725758)

### Commit Info
| Context | Commit | Description |
|---------|--------|-------------|
| RUN | [9146691e](https://github.com/huggingface/transformers/commit/9146691e4ecd1fec6bb61344b8ec840921990827) | workflow commit (merge commit) |
| PR | [ed6659d1](https://github.com/huggingface/transformers/commit/ed6659d15e5aa31d0311b84a76f56e2cf673d168) | branch commit (from PR) |
| main | [67538ec6](https://github.com/huggingface/transformers/commit/67538ec6a42ea2c8fdb99301b22a9b313d4741b1) | base commit (on `main`) |

⚠️ No test being reported (jobs are skipped or cancelled)!


[Workflow Run ⚙️](https://github.com/huggingface/transformers/actions/runs/28879951771)

This comment contains `run-slow`, running the specified jobs: 

models: ["cli"]
quantizations: []

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---

### CI recap

**Dashboard:** [View test results in Grafana](https://transformers-ci.lor-e.huggingface.cool/d/pytest-observability-by-pr/pytest-observability-branch?var-pr=46267)
**Latest run:** [28878533761:1](https://github.com/huggingface/transformers/actions/runs/28879934896)
**Result:** `success` | **Jobs:** 3 | **Tests:** 205 | **Failures:** 1 | **Duration:** 2m 6s

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## CI Results
[Workflow Run ⚙️](https://github.com/huggingface/transformers/actions/runs/28879951771)

### Commit Info
| Context | Commit | Description |
|---------|--------|-------------|
| RUN | [b41f8131](https://github.com/huggingface/transformers/commit/b41f81310580fa860bb6776eeaa2d55ee4c6115d) | workflow commit (merge commit) |
| PR | [b4782bcd](https://github.com/huggingface/transformers/commit/b4782bcdafd635cfa987452766579104a6de5364) | branch commit (from PR) |
| main | [67538ec6](https://github.com/huggingface/transformers/commit/67538ec6a42ea2c8fdb99301b22a9b313d4741b1) | base commit (on `main`) |

✅ No failing test specific to this PR 🎉 👏 !