In principle, as long as the side panels do not receive the experimental status, you use a content script , to install large marginor paddingone hand bodyor htmlinsert an element position: fixedin the current page, superimposed on this field, and then draw it.
Everything that needs to be saved between pages is saved in the extension, and each time you recreate a pseudo-sidebar when the page loads.
See Firebug Lite or StumbleUpon extensions for examples.
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