The goal is to handle traffic spikes gracefully without provisioning additional searcher nodes: when the local search queue is saturated, overflow splits are transparently routed to Lambda for processing.

The offloading decision happens **on the leaf side**, inside the `SearchPermitProvider`. The permit provider already manages a bounded queue of pending split search tasks (gated by memory budget and download slots). When a leaf search request arrives, the provider checks the current queue depth against a configurable `offload_threshold`. If granting permits for all requested splits would exceed this threshold, only enough splits to fill up to the threshold are processed locally — the rest are marked for offloading.

The offloaded splits are batched (up to `max_splits_per_invocation` splits per batch, balanced by document count) and sent to Lambda in parallel. Each Lambda invocation runs the same leaf search code path and **returns per-split results individually**. This is important: the per-split responses are fed back into the `IncrementalCollector` and populate the **partial result cache**, so subsequent queries hitting the same splits benefit from cached results regardless of whether the split was searched locally or on Lambda.

Depending on the configuration, the Lambda function code can be **deployed automatically** at startup. The `quickwit-lambda-client` crate embeds a compressed Lambda binary at compile time. When `auto_deploy` is configured, Quickwit will:
1. Check if a published Lambda version matching the current binary already exists (identified by a description tag `quickwit:{version}-{hash}`)
2. Create or update the function and publish a new version if needed
3. Garbage-collect old versions (keeping the current one + 5 most recent)

This ensures the Lambda function always matches the running Quickwit version without any external deployment tooling. Manual deployment is also supported for users who prefer to manage Lambda functions through Terraform or other IaC tools.

Lambda offloading is opt-in. Add a `lambda` section under `searcher` in the node configuration:

```yaml
searcher:
  lambda:
    offload_threshold: 100     # queue depth before offloading kicks in (0 = always offload)
    max_splits_per_invocation: 10
    auto_deploy:
      execution_role_arn: arn:aws:iam::123456789012:role/quickwit-lambda-role
      memory_size: 5 GiB
      invocation_timeout_secs: 15
```

- **`quickwit-lambda-client`**: Handles Lambda invocation (with metrics) and auto-deployment logic. Embeds the Lambda binary at build time.
- **`quickwit-lambda-server`**: The Lambda function handler itself — receives a `LeafSearchRequest`, runs `multi_index_leaf_search`, and returns per-split `LeafSearchResponse`s.

- **`quickwit-search`**: New `LambdaLeafSearchInvoker` trait; `SearchPermitProvider` gains `get_permits_with_offload` to split work between local and offloaded; `leaf.rs` orchestrates local and Lambda tasks in parallel.
- **`quickwit-config`**: New `LambdaConfig` and `LambdaDeployConfig` structs under `SearcherConfig`.
- **`quickwit-serve`**: Initializes the Lambda invoker at startup when configured.
- **`quickwit-proto`**: New `LeafSearchResponses` wrapper message for batched per-split responses.

build fix