Snowflake MCP connector shows stale 'requires authentication' status when actually working

## Description

The system-reminder list of MCP servers that "require authentication before their tools can be used" incorrectly lists a Snowflake connector as blocked, even when a live tool call against that same connector succeeds immediately with no auth error.

## Steps to reproduce

1. In a session where a Snowflake MCP server is configured and its OAuth/token state is actually valid, note that the system reminder still lists it under "The following MCP servers require authentication before their tools can be used."
2. Call the connector's SQL execution tool directly with a trivial query, e.g. `SELECT CURRENT_TIMESTAMP()`.
3. The call succeeds immediately and returns a valid result — no authentication error, no OAuth prompt needed.

## Expected behavior

The "requires authentication" listing should reflect live connector state, or at minimum should not be shown once a tool call against that server has succeeded in the session.

## Actual behavior

The stale listing persists across turns (and apparently across sessions) even after a successful call proves the connector is authenticated and working. This has caused real harm: a session took the listing at face value and told the user to reauthorize outside the session without ever attempting a call, costing investigation time on a task that depended on that connector for data access. This has now been observed as a repeat pattern across multiple independent sessions.

## Impact

Agents (and by extension users) are misled into believing a working data-access path is unavailable, leading to unnecessary reauthorization steps, abandoned investigation paths, or incorrect "blocked" reporting to the user.

## Suggested fix

Either refresh the "requires authentication" status against a live check before surfacing it in the system reminder, or suppress/update the listing for a server as soon as any tool call against it succeeds within the session.

Start by locating the code that generates the system-reminder authentication listing and tracks MCP server state, then reproduce the issue with a configured Snowflake server and a successful SQL execution tool call. Done means the reminder reflects the live state or stops claiming authentication is required after a successful call, with the stale-status behavior covered by the relevant tests.

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