"google.com/search/hello motto" is not a valid URL for two reasons.
1. To be a URL it must contain a scheme (like http or https).
2. URLs may not contain spaces. They are represented by %20 instead.
You can read over the information for what makes a valid URL at the Wikipedia page.
https://en.wikipedia.org/wiki/URL
As you pointed out, what you really wanted was https://google.com/search/hello%20motto, which is a URL.
Privacy Browser does automatic recognition of partial URLs. For example, if you had typed "google.com/search/hello%20motto", Privacy Browser would have recognized that, if a valid scheme was added, that would be a URL and would have done such.
Alternatively, if you had typed "https://google.com/search/hello motto" Privacy Browser would have recognized that if the space was replaced by a %20 it would be a valid URL and would have done the substitution.
This URL recognition is all handled by the Android pattern URL matcher.
https://developer.android.com/reference/android/util/Patterns#WEB_URL
Any more aggressive attempt to turn what the user types into URLs would inappropriately turn what the user intends to be a search with the default search engine into URLs that the user didn't intend. So, there is nothing unexpected about this behavior and it is indeed doing exactly what it should do.
As a further point, even though https://google.com/search/hello%20motto is a valid URL, it is not a URL that matches Google's system, so that if you attempt to go to it, Google will respond with a 404 error.
The URL you would want to do a Google search is https://www.google.com/search?q=hello%20motto. Just like the two examples above, if you partially enter the URL, Privacy Browser will auto correct it to a full URL. However, if you just want to do Google searches, I would recommend you change the search engine in Privacy Browser's settings to Google and then you can simply type "hello motto".
