Smarter output logging between server connections

[bmingles]

The JSapi client currently dumps all existing server output whenever a connection is made. In the vscode extension, this can be a little odd if the user has previously connected and disconnected since the output is already higher up in the terminal. Do we want to do something different here like maybe truncate the log if it has already been shown in the current vscode session?

Created deephaven/deephaven-core#5694 to expose more controls for logging subscriptions.

Also it has been reported that the layout of the output does not match the panel size.
deephaven/deephaven-core#5937