[FEATURE]: Redesign Connection Management for Better Pooling and Context Isolation

[jac0626]

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Description:
The current Connections singleton mixes configuration (aliases) with active connection state. As we move towards a stateless GrpcHandler, the connection management layer needs to be fundamentally redesigned to better support:

1. True Pooling: Manage a pool of underlying gRPC channels that can be borrowed.
2. Context Isolation: Ensure that user-specific context (like db_name, user, role) is applied at the request level, not the connection level.
3. Health Checks: Better active health monitoring of connections.

Note: This is a long-term refactoring goal that builds upon the work of making GrpcHandler stateless .

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