Thanks for sharing the link. We believe to have understood the page you are getting has a different layout than the one you linked in the other post on this forum. That’s because the page /book-now-3 renders the Shortcode of type “Search Form”, which is different than the widget/block “Search Form”.
You should work on the settings of the widget/block to control the landing page where the booking process will actually start, by clicking the toolbar button to change the dates is always allowed, and that link will always take the users to the “Search Form” shortcode. In your case there are some CSS conflicts with your theme, which is also styling the drop down menus (select tags) through JavaScript (jQuery) plugins. You should probably work on the settings of your Theme to get the desired layout and behaviour.