Kind of, however the Google Search Bar present on website is usually there to search across their domain, the search results are limited to their domain e.g exa

Kind of, however the Google Search Bar present on website is usually there to search across their domain, the search results are limited to their domain e.g example.com/page1, example.com/page2. Google will carry on supporting this. What they are ending is their support for websites to search across the entire web. The websites that search across the entire web are usually niche search engine websites.