Python SDK v2

I'll use this issue to add notes about what I think should happen for V2.

Use snake case instead of camel case on types.py (mcp.types.Tool is not following python's naming convention #97)
Don't use RootModel on types.py - It makes hard to reason about types.
Revisit generic classes, and add more default values for them Excessive use of generics #1207
Rethink ClientSessionGroup. It doesn't have a user-friendly API.
Rename FastMCP to MCPServer.
Add conveniences for MCP proxy pattern #12

I'll lock the issue, so only maintainers can comment, and I can focus on the things that I really think should be here.

I'll use this issue to add things I see as well.

@maxisbey

Checklist

Low level parameter callbacks (@maxisbey is working on it)
We do need the idea that is presented here: Pluggable Transport Abstractions #1591, but with a better pattern. I did explain this on the discord - details should be in the python and transport channel.
We need to improve the documentation. This needs to be a continuous effort, which we didn't create the habit yet.
- Making the README simple - all the examples should be in the documentation.
We need to recheck the constructor parameters of the the MCPServer class. I did remove and refactor a bit, but we need to audit it a bit better.
MCP Proxy, as mentioned above.
Refactor the auth "way of using it".
- Drop the use of Field(description=...), and use proper docstrings. As far as I know, we are not creating json schemas from it, so it's useless.
Simplify/remove/(move to docs) the current examples. My suggestion here would be to take the opportunity on docs write, to actually check the examples, and try to move them to the docs.
- Check how FastAPI does it - they have a docs_src where they put all their code examples, and they actually run tests on every snippet in tests.
- Check other projects that do inline markdown snippet, like pydantic-ai.
Create dependency injection in MCPServer.