[Doc][4/N] Reorganize API Reference (#11843)

Signed-off-by: DarkLight1337 <tlleungac@connect.ust.hk>

docs/source/api/engine/async_llm_engine.md

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+# AsyncLLMEngine
+
+```{eval-rst}
+.. autoclass:: vllm.AsyncLLMEngine
+    :members:
+    :show-inheritance:
+```

docs/source/api/engine/index.md

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+# vLLM Engine
+
+```{eval-rst}
+.. automodule:: vllm.engine
+```
+
+```{eval-rst}
+.. currentmodule:: vllm.engine
+```
+
+```{toctree}
+:caption: Engines
+:maxdepth: 2
+
+llm_engine
+async_llm_engine
+```

docs/source/api/engine/llm_engine.md

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+# LLMEngine
+
+```{eval-rst}
+.. autoclass:: vllm.LLMEngine
+    :members:
+    :show-inheritance:
+```

docs/source/api/multimodal/index.md

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+(multi-modality)=
+
+# Multi-Modality
+
+```{eval-rst}
+.. currentmodule:: vllm.multimodal
+```
+
+vLLM provides experimental support for multi-modal models through the {mod}`vllm.multimodal` package.
+
+Multi-modal inputs can be passed alongside text and token prompts to [supported models](#supported-mm-models)
+via the `multi_modal_data` field in {class}`vllm.inputs.PromptType`.
+
+Looking to add your own multi-modal model? Please follow the instructions listed [here](#enabling-multimodal-inputs).
+
+
+## Module Contents
+
+```{eval-rst}
+.. automodule:: vllm.multimodal
+```
+
+### Registry
+
+```{eval-rst}
+.. autodata:: vllm.multimodal.MULTIMODAL_REGISTRY
+```
+
+```{eval-rst}
+.. autoclass:: vllm.multimodal.MultiModalRegistry
+    :members:
+    :show-inheritance:
+```
+
+### Base Classes
+
+```{eval-rst}
+.. automodule:: vllm.multimodal.base
+    :members:
+    :show-inheritance:
+```
+
+### Input Classes
+
+```{eval-rst}
+.. automodule:: vllm.multimodal.inputs
+    :members:
+    :show-inheritance:
+```
+
+### Audio Classes
+
+```{eval-rst}
+.. automodule:: vllm.multimodal.audio
+    :members:
+    :show-inheritance:
+```
+
+### Image Classes
+
+```{eval-rst}
+.. automodule:: vllm.multimodal.image
+    :members:
+    :show-inheritance:
+```
+
+### Video Classes
+
+```{eval-rst}
+.. automodule:: vllm.multimodal.video
+    :members:
+    :show-inheritance:
+```

docs/source/api/offline_inference/index.md

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+# Offline Inference
+
+```{toctree}
+:caption: Contents
+:maxdepth: 1
+
+llm
+llm_inputs
+```

docs/source/api/offline_inference/llm.md

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+# LLM Class
+
+```{eval-rst}
+.. autoclass:: vllm.LLM
+    :members:
+    :show-inheritance:
+```

docs/source/api/offline_inference/llm_inputs.md

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+# LLM Inputs
+
+```{eval-rst}
+.. autodata:: vllm.inputs.PromptType
+```
+
+```{eval-rst}
+.. autoclass:: vllm.inputs.TextPrompt
+    :show-inheritance:
+    :members:
+    :member-order: bysource
+```
+
+```{eval-rst}
+.. autoclass:: vllm.inputs.TokensPrompt
+    :show-inheritance:
+    :members:
+    :member-order: bysource
+```

docs/source/api/params.md

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+# Optional Parameters
+
+Optional parameters for vLLM APIs.
+
+(sampling-params)=
+
+## Sampling Parameters
+
+```{eval-rst}
+.. autoclass:: vllm.SamplingParams
+    :members:
+```
+
+(pooling-params)=
+
+## Pooling Parameters
+
+```{eval-rst}
+.. autoclass:: vllm.PoolingParams
+    :members:
+```
+