Is it possible to hide the icon in Dock Bar under MacOS?
No. Eddie keeps a normal Dock icon on purpose.
Under MacOS, only background agent apps can omit the Dock icon (for example with LSUIElement). Agents are not treated as foreground apps: on logout or shutdown the system does not wait for them to finish cleanup.
Eddie must be able to restore settings (for example deactivate Network Lock) before the session ends. That requires a foreground application, so the Dock icon cannot be hidden while still behaving safely.
Apple Tech Support has confirmed that you cannot both hide the Dock icon / menu bar and remain a foreground app that can cancel or complete shutdown cleanup.
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