[MCP] Respond to stdio initialize before metadata inference

[Souvik Ghosh (Souvik04)]

Why make this change?

Fixes #3430.

MCP stdio currently performs database schema introspection before entering the JSON-RPC read loop. For remote databases with many entities, clients can time out waiting for the initialize response even though the process and database are healthy.

Related: #3783 and #3784. This change also ensures stdio initializes metadata providers without starting the HTTP host.

What is this change?

• Enter the MCP stdio protocol loop before database metadata inference and tool registration.
• Defer that work until the first tools/list or valid tools/call request.
• Cache the initialization task so repeated requests cannot run inference more than once.
• Await initialization before reading or executing tools, including metadata-enriched custom tool schemas.
• Add a deterministic test that blocks metadata inference and verifies initialize responds while tools/list remains pending.

How was this tested?

• Integration Tests
• Unit Tests

Focused MCP stdio and registry suite: 49 passed, 0 failed.

dotnet format --verify-no-changes and git diff --check also pass.

Sample Request(s)

Send initialize, notifications/initialized, then tools/list over stdin. The initialize response is emitted immediately; tools/list waits until schema inference and tool registration complete.

{"jsonrpc":"2.0","id":1,"method":"initialize","params":{"protocolVersion":"2025-11-25","capabilities":{},"clientInfo":{"name":"probe","version":"1"}}}
{"jsonrpc":"2.0","method":"notifications/initialized","params":{}}
{"jsonrpc":"2.0","id":2,"method":"tools/list","params":{}}

[azure-pipelines]

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[Souvik Ghosh (souvikghosh04)]

Superseded by #3805, opened from the Azure repository branch under the CODEOWNER account Souvik Ghosh (@souvikghosh04).