Open it in a window
The side panel's content in a window of its own, with a tab for each page it reads.
Press Open in a window on the bar, or the window button at the top right of the side panel, to show the same content in a window of its own, to keep beside the page on a second screen. The side panel beside the page closes, so the panel is in one place at a time. A panel opened this way stays with its tab instead of following you, and has a Dock to the side panel button that closes the window and opens the side panel again.
The window shows which page it is reading in a row of tabs along its top, with each page's icon and title. Open the window from another tab and that tab joins the same window rather than opening a second one; click a tab (or use the arrow keys) to switch between them, and the page comes to the front in its own window. Close a tab in the row with its ×, or with Delete. A tab closed in the browser leaves the row, and the window closes with its last tab.
Questions
Can I keep the panel on a second screen?
Yes. Open in a window shows the same content in a window of its own, and the side panel beside the page closes.
How do I put it back beside the page?
Press Dock to the side panel in the window. It closes the window and opens the side panel again.