I think it's not possible in wordpress to make 2 different result pages and make them both work correctly – I'm not familiar with the concept.
You can try to enable the “Override the default WordPress search results page?” option on the General Options -> Behavior panel, but there is a good chance it still won't work.
Multisite posts are stored in different database tables, so the internal get_post($id) wordpress call is not able to parse them across another site, and I believe that's why you don't have any results if the term is outside the site.
Unfortunately I don't think any solution exists to that yet.
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