V2: Redesign HTTP client lifecycle management with MCPClient/Client approach

[felixweinberger]

Context

Following discussion in #1177, @Kludex raised concerns about the current API approach for HTTP client handling.

Problem

The current pattern of accepting an HTTP client directly may not be the cleanest long-term approach. While many LLM providers do this, there are concerns about API sustainability.

Proposed Direction

Create an MCPClient/Client class that manages the lifecycle of the HTTP client internally, rather than accepting it as a parameter. This is similar to how Starlette's TestClient works.

Key points from @Kludex:

• The SDK should manage HTTP client lifecycle internally
• Could use composition (not necessarily inheritance)
• Reference implementation: Starlette's TestClient pattern
• Allow passing configuration parameters rather than the client itself

cc @Kludex @maxisbey

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Reference: #1177

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Update: This is being addressed as part of #1728 (ergonomic test client). We're creating a unified Client class that handles both in-memory testing and HTTP production use cases.

[maxisbey]

Closing as completed by #1870

pls reopen if you think we should @felixweinberger