[DropDownTree] Filter input should persist the value entered by the user

[yanmariomenev]

Describe the bug Currently, the filter input is cleared after the popup closes. However, when the popup is reopened, the list remains filtered based on the user's last input, even though the filter input field does not retain the previous filter value. This behavior persists in both of our data binding directives.

To Reproduce Open - https://www.telerik.com/kendo-angular-ui/components/dropdowns/dropdowntree/filtering/#toc-filtering-with-the-hierarchy-binding-directive

1. Open the popup

2. Enter a filter value

3. Close the popup without selecting any value

4. Open the popup again, data is still filtered even though the filter value is empty

An older working version that clears the filter input and list - https://stackblitz.com/edit/angular-p7kflb-i2wsj8?file=app%2Fapp.component.ts

Expected behavior The popup list filtering should be cleared when closing the popup.

However, this leads to another question regarding our other libraries, as they persist the filter input state and filter list state: https://www.telerik.com/kendo-react-ui/components/dropdowns/dropdowntree/filtering/ https://demos.telerik.com/kendo-ui/dropdowntree/client-filtering

We should consider which behavior to keep and fix the filtering behavior of the component.