Implement Python inference and inflation library

Build the central Python SDK responsible for managing the request-time lifecycle of a template-based UI.a

Proposed tasks:
- [ ] Automated Prompt Builder: Create a utility to ingest template libraries and extract minimal schemas for LLM system prompts: https://github.com/nan-yu/A2UI/blob/c319fe70337c0a041ae0c7933bc95e5d7b94afcc/agent_sdks/python/src/a2ui/core/template/manager.py.
- [ ] Inflation: Implement logic to traverse a template and replace all `{{}}` placeholders with literal values from the LLM's data model.
- [ ] Handle the logic for mapping LLM-returned `templateName` to the local template storage.
- [ ] **Optional**: Support native data binding by leveraging the [dataModelUpdate](https://github.com/google/A2UI/blob/main/specification/v0_8/json/server_to_client.json#L70) schema, allowing the client to resolve placeholders reactively.