[Tracking Issue] MCP server performance profiling prompt experiment

**DevTools tracking issue for https://github.com/dart-lang/ai/issues/417**

## Introduction

This is a tracking issue for adding a performance profiling prompt, e.g. `analyzeFlutterPerformance` to the Dart MCP server.

## Scope

The initial scope of this feature is medium. The goal is to ship the prompt quickly, evaluate its effectiveness, and refine the data and steps as necessary. Please see [go/ai_assistance_devtools](http://goto.google.com/ai_assistance_devtools)

Start with the linked dart-lang/ai issue #417 and the DevTools MCP server context; the issue does not name a file, test, or entry point. Confirm the prompt's initial scope and evaluation plan from the issue and referenced go/ai_assistance_devtools material; done means the profiling prompt is shipped for evaluation.

Written by the indexing model from the issue text.