When I open system settings in sidebar view mode, I can search immediately because search field is auto-focused. However search field is not auto-focused when I set tree or icon view.
Tree view also doesn't have initial startup focus on search field, also there is no focus on search field in icon and tree views after changing to this layouts in hamburger menu - Configure - General Operating System: KDE neon Developer Edition KDE Plasma Version: 5.14.80 KDE Frameworks Version: 5.53.0 Qt Version: 5.11.2 Kernel Version: 4.15.0-39-generic
Tree view no longer exists but I can confirm that icon view the search field isn't focussed when System Settings is started. Operating System: KDE neon Unstable Edition KDE Plasma Version: 5.20.80 KDE Frameworks Version: 5.76.0 Qt Version: 5.15.0
*** Bug 431989 has been marked as a duplicate of this bug. ***
Icons view is being removed for Plasma 6, so this bug will be no longer possible to experience there. :)