feat: add Pydantic AI extended sample

[simple-agent-manager]

Summary

• Adds a new pydantic-ai-extended sample: a multi-service AI app built with Pydantic AI, FastAPI, PostgreSQL (pgvector), and Redis
• Follows the same architecture as the mastra-extended sample, adapted for the Python ecosystem
• Background worker generates sample support tickets and system alerts, classifies them with an LLM, and stores vector embeddings for semantic search
• Pydantic AI copilot agent with tools (get_tickets, get_alerts, get_tags, search_items) inspects database state before answering questions
• Supports Docker Model Runner for local dev (compose.dev.yaml) and Defang managed model providers for deployment (compose.yaml)
• Fixes the chat composer layout so the input/button controls keep stable dimensions after a streamed response

Architecture

Service	Purpose
app	FastAPI web app serving UI + API
worker	Background job processor (classify + embed)
postgres	pgvector-enabled PostgreSQL
redis	Job queue
chat	Defang managed chat model
embedding	Defang managed embedding model

Closes #638

Screenshots

Playwright screenshots captured against the sample UI with successful mocked API responses, after fixing the chat composer layout. Screenshot assets are on temporary branch sam/pydantic-ai-extended-screenshots-01kr0y.

Dashboard

Copilot chat

Mobile

Test plan

• python3 -m compileall app
• Playwright UI screenshot capture for dashboard, chat, and mobile states
• docker compose -f compose.dev.yaml up --build starts all services (blocked in this workspace: docker, podman, PostgreSQL, Redis, and /var/run/docker.sock are unavailable)
• Docker Model Runner chat + embedding services respond locally (blocked by unavailable Docker runtime)
• Generate sample items button creates 10 tickets + 10 alerts against real local services
• Worker classifies and embeds all items against real local services
• Copilot chat answers questions using tool calls against real local services
• Compose structure passes CI validation checks
• README metadata fields present (Title, Short Description, Tags, Languages)

🤖 Generated with Claude Code

Samples Checklist

✅ All good!