opening a new tab should use current tab's connection not the connection of the last executed query
A new tab's connection is based on the connection of the last executed mongo command. Seems to me to make more sense if the new tab's connection is based on the currently active tab's connection. The user's brain is solving a problem in the current tab, so if they request a new tab it is very likely that she is thinking in that context rather than the connection from potentially many tabs in the past.
An even simpler example: with multiple tabs open each with a different connection, execute a query in a tab #1. Then close tab #1. You return to tab #2 and continue working on the code but without executing any queries. Then open a new tab -- it will use the connection of closed tab #1. That strikes me as unintuitive, even surprising.