To prevent authenticated external users from searching for Quote and Contract objects but not Opportunity or Asset objects, you need to remove Opportunity and Asset from the object list in the Global Search Result component property editor and the Autocomplete object list in the Search component property editor. The Global Search Result component displays the search results for all objects that match the search term. The Autocomplete object list displays the suggested objects that match the search term as you type. You can customize these components by selecting or deselecting the objects that you want to include or exclude from the search.