How can I just show the preview panel without the note edit panel?

Open Settings > Interface > Layouts, select the layout, and choose Note preview as its central widget.

You can create a new layout first with Add from current, or use Add from preset... and select the Preview only preset.

Afterward, turn off the note edit panel in the Window > Panels menu. The preview will automatically use the available central area.

Keep in mind that you can move around all panels as you like by clicking Window / Unlock panels in the main menu. You can also resize all panels to fit your needs.