Search page is not created

I am building a blog, plan to switch to a CMS plan but search should be able to be created and styled as far as I know with no plan. I have a search button but it leads straight to the 404 page and there is no search page in the utility page options. I know that the search will be non-functional but I want to have it set up in principle and don’t really want to set up a plan and still be unable to search.

Here is my site Read-Only: LINK
(how to share your site Read-Only link)

If you’re using a free workspace and unhosted site you may not be able to active search fully. Usually, when you drop a search control on the page, the search utility page is also created and you can customize it.