Hi @YakovVoloch thanks for reaching out.
Can I confirm you are referring to the managed version of Chrome browser (i.e. Chrome Enterprise) whereby it's employees within an organisation accessing AI/Google Search from a managed Chrome browser?
Either way, it sounds the policies you used are working as intended for the browser, but to change the Search Page, you'll need to look at your Workspace Service settings rather than Chrome Browser policies.
There's a few tips below, however for further questions we would recommend you check out the Workspace community specifically here.
If your users are on Workspace accounts, AI Overviews are often tied to whether "Search Customization" or specific "Data and Personalization" flags are enabled in the Google Admin Console.