if you cannot load the whole page for any reason, that's a failure of design. use pagination, that has existed since the 90s.
The content you can find wih the browser search still doesn't do d the text on another page. A custom search could including a jump to the page.
Forcing a request what could be done locally is bad design.
The dedicated search field is for searching my websites and the result would be a list of my pages that contain the search term. Ctrl-F jumps to the location of the search term on the page I'm already at.