Ctrl + G certainly is hookable[0], folks just rarely know that it's an alias for 'find'. If you REALLY want the browser's search, in Chrome, you can use the mouse to open the menu and choose "Find". You could also use any keyboard shortcut that focuses the URL bar (so keyboard events are no longer sent to the page) and press Ctrl-f then.

0: In Google Sheets, for example, Ctrl-g opens the JS-driven find bar, or, if it's already open, advances the match.