Thanks for the suggestion. This has now been implemented and will be included in the next Objo Studio release: https://feedback.objo.dev/feature/1175
The AI Assistant can be opened in a separate, resizable window and moved to another monitor. It can be docked back into Studio at any time without losing the conversation, and Studio remembers the preferred mode, size, and position.
Each open solution has its own independent assistant window and conversation.
To dock and undock, use the ellipsis button in the AI Assistant at the top to toggle between docked and undocked:

