Context: Currently, Atlas only supports connecting to standard and standardSrv connection strings. 

In Atlas CLI, we support also connecting to private and privateSrv. Here's a sample PR of how we could do this in the MCP Server https://github.com/mongodb-js/mongodb-mcp-server/pull/631/files#diff-f557a7c89cd87cd0ffac8c1e483f02909070e2067d6d2591ccba18e499f42557R87-R99

Goal: The goal of this task is to support that the MCP server can also connect to private connection strings or privateEndpoint connection strings if that is provided as an argument.

Support targets:

• standard -> standard || standardSrv
• private -> private || privateSrv
• privateEndpoint -> connectionString || srvConnectionString ( from the clusters connection string object in ClusterDescriptionConnectionStringsPrivateEndpoint)

Tech details

Draft PR for private endpoint support https://github.com/mongodb-js/mongodb-mcp-server/pull/631 - not a mandatory implementation design, just illustrative

OpenAPI object from cluster description

ClusterDescription20240805 -> ClusterConnectionStrings -> privateEndpoint -> connectionString
ClusterDescription20240805 -> ClusterConnectionStrings -> private