I've performed some tests on my website and it seems that the option to control URL when search results update, isn't available when a view is being edited using the new block editor.
I've shared this with the concerned team for further review and will keep you updated through this ticket.
Meanwhile, if that option is important, you can re-create the view using the classic views editor (Toolset -> Views) and then you'll be able to control that option.
Adding to my previous message, there is a global option "Enable history management settings for AJAX custom search", which can be disabled from WP Admin -> Toolset -> Settings -> Front-end Content.
( screenshot: hidden link )
It's important to note that this option will work for all views on the website, which are set to update results using AJAX and the URL will stay the same.