When an application is launched in the Modern theme, there is no search button in the toolbar.
The reason for this is the changes made to the tl:TabSwitchCommandModelConfiguration by ticket #26373. Previously, an image could be configured for the button at the tl:TabSwitchCommandModelConfiguration. Previously, IMAGE_BUTTONS_SEARCH_SIMPLE was configured as the icon for the search. After the changes made by ticket #26373, the icon of the legacyTabbar.template.xml arguments is used.
The layout of the search is defined in searchInput.layout.xml. The icon for the button is IMAGE_BUTTONS_SEARCH22. In the Modern theme, the IMAGE_BUTTONS_SEARCH22 variable does not exist, so the tl:ThemeImage$NoIcon is used, which adds a style="display:none" when rendering the button. This will not display a button for the search.
Test
Run demo in Modern theme and check if the button is visible for search.