[v3-beta] Improve conversation management UI

[dlqqq]

Problem

The current conversation management UI needs to be enhanced before the v3.0.0 official release.

Users should be able to see a list of current conversations in the UI, and should be able to click into a chat directly. These capabilities should not be provided exclusively by a HTML dropdown.

Proposed Solution

Reach a consensus on a good UI to provide for conversation management.

Additional context

See #813 for additional discussion & proposals from other contributors.

This is a very short issue; I hope to expand this once we have time to work on this.