Hi,
When using the settings or the results shortcodes, the corresponding search bar needs to be present on the page as well. The automatic replacement feature will replace the theme search with the given search bar globally.
You can use multiple search bars of course, but the replacement can only use one. If you want some sort of a condition to show the searches depending on the pages, then I would rather suggest using the search widgets, or the shortcodes – depending on the situation.
Some themes have conditional widget, where you can select which widgets should be visible on which page – you could use the search widget that way.
If you use a page builder of some sort, and it allows using shortcodes/text blocks where you need the search, you can simply put the corresponding shortcode there.