Sticky In-Page Search Results

Exactly what I am doing as well.

Yes. Or even better open a new tab, like with browsers, to have full window width available? This is similar to open a new Logseq window, without performance consequences and no focus shift due to multiple windows.

(Update) Related: [Partial Done] Add tabbed windows to desktop client / Multiple instances of Logseq

IMO this should be a native Logseq feature.