Add analyzer fix support to Azure SDK MCP

There were several projects related to this in the .NET repo, all of which are in different states of completion. There were two projects that were supposed to make it so these errors would not need to be fixed at this layer, but those two projects pivoted and are no longer addressing this problem, so these errors need to be addressed here.

Some information:
- Many of our analyzers have Roslyn code fixers, the ones that don't, work is in progress to add them (lower priority but it has been happening)
- Our analyzer project is slowly being migrated from the azure-sdk-tools repo to the azure-sdk-for-net repo, we were struggling with the dev loop, you couldn't easily see what errors needed to be fixed in SDK code across the repo while working on the analyzer project
- We do have an MCP server that has been used to fix analyzer errors in MCP tools: https://github.com/Azure/azure-sdk-for-net/tree/main/sdk/tools/Azure.GeneratorAgent

I have an untested draft where I was looking at a starter implementation that solely uses prompts https://github.com/Azure/azure-sdk-tools/pull/15425, but it would really be nice to hook in the analyzer fixers and some of the deterministic pieces if possible. There is also a classifier MCP tool. I didn't have enough time to map out how the integration would actually work, it does seem difficult since most of these pieces are partially done and not easy to link together. But I did have an idealistic vision of making a really nice end to end implementation here where everything was shared and it's a blend of determinism/LLM when appropriate, I just didn't know exactly how to get there.

Start by reading sdk/tools/Azure.GeneratorAgent and the draft implementation in azure-sdk-tools PR 15425, then inspect the referenced analyzer fixers, deterministic pieces, and classifier MCP tool. Map how these partially completed components could connect; done requires a defined end-to-end integration that uses analyzer fixes where available and prompts or deterministic handling as appropriate.

Written by the indexing model from the issue text.