feat(examples): Add Federated Analytics example

[chongshenng]

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[Copilot]

Pull request overview

This PR adds a new example demonstrating Federated Analytics using Flower's framework. The example shows how to perform distributed statistical analysis on healthcare data stored in multiple PostgreSQL databases without centralizing the raw data.

Changes:

• Implements a federated analytics pipeline that computes aggregated statistics (mean and standard deviation) across distributed databases
• Provides database setup scripts to generate artificial OMOP CDM-compliant healthcare data
• Includes comprehensive documentation for running the example with Flower's Deployment Engine

Reviewed changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
examples/federated-analytics/pyproject.toml	Defines project dependencies and Flower app configuration for the federated analytics example
examples/federated-analytics/federated_analytics/task.py	Implements database querying and feature aggregation logic for computing distributed statistics
examples/federated-analytics/federated_analytics/server_app.py	Defines the ServerApp that orchestrates the federated analytics workflow
examples/federated-analytics/federated_analytics/client_app.py	Defines the ClientApp that queries local databases and computes partial statistics
examples/federated-analytics/db_start.sh	Bash script to generate and start multiple PostgreSQL containers using Docker Compose
examples/federated-analytics/db_init.sh	Database initialization script that creates tables and populates them with synthetic healthcare data
examples/federated-analytics/README.md	Provides setup instructions and usage guide for the federated analytics example

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