The search-fields and searchbutton generate a list using microflow xyz. The datagrid uses the same microflow xyz. Otherwise the grid is not related to the result of the run of the microflow when triggered by the searchbutton. That is the reason why it is not updating.
It is probably easier to include the search-fields in the entity that you show in the datagrid, if you haven’t already, and then go to the domain-model, right-click the entity and select “Generate overview pages”. Once that is done, open the overview page, remove the attributes that you don’t want to show in the searchfields, remove the attributes that you don’t want to show in the datagrid, and you have the page you seem to want.
See https://docs.mendix.com/howto/front-end/create-your-first-two-overview-and-detail-pages#3-creating-overview-detail-pages-automatically for a howto on generating the overview page.