I have reviewed the app you mentioned, but its widget only offers favorite spots, not favorites and search any locations combined (looks to me, that is not a search, but filter).
Unfortunately, the Apple API does not permit this, which is disappointing because having favorites listed first would be beneficial.
I recommend exploring iOS focus mode. You can create separate focus modes for private and public use, organizing different apps and widgets on your home screen to enhance privacy (https://support.apple.com/en-gb/guide/iphone/iphd6288a67f/ios).
Regrettably, I am unable to provide further assistance at the moment.