@Cr8zy_Ivan@fedia.io No, unfortunately - see & vote for https://bugzilla.mozilla.org/show_bug.cgi?id=1502713. (I use BSP2, too.)

I doubt any extension could do it either (new WebExtension API deems such behavior/functionality insecure/too privileged).

I hope it could be customizable by "user.js" or a similar javascript file put in your Firefox profile. If anyone finds anything, report here, please.

Partial alternative: Right click at BSP2 icon > "Open BSP2 in a Tab". Potentially pin the tab. Then Ctrl+TAB to switch back and forth. For other extensions, figure out "moz-extension://..." URL to their files shown in the sidebar. It may not work exactly well/same as in a sidebar (or it may work better).