Can't select text displayed in the sidebar

I think text selection might be disabled by the browser style (see Browser styles on MDN). By default, sidebars also use the browser’s stylesheets for extensions which, among other things, disables text selection.

You can opt-out of this by specifying browser_style: false in your extension’s manifest.json like so:

{
    "manifest_version": 2,
    "name": "Context Search",

    "sidebar_action": {
        "browser_style": false,
        ...
    },
    ...
}

(See sidebar_action on MDN)