Android behavior is to show the keyboard when a text field gets focus. See Handling Keyboard Input in the Android docs:
The Android system shows an on-screen keyboard—known as a soft input method—when a text field in your UI receives focus.
If you don't want the keyboard to show up until the user touches the box then the natural way to do that is to make sure the focus starts elsewhere. How to do that will depend on your app layout and if your search-box is in a BlazorWebView or if it's in the surrounding Xaml. At the XAML level, you can call Focus on another control (a VisualElement), with the caveat that Focusing on a container may pass focus down to its first child that can take focus, which may end up back to your searchbox. Instead, you may want to set focus at the Blazor level on a control such as a button inside the web view.