[PickerInput]: can't select items if datasource api return list only if search is typed

[AlekseyManetov]

Description (optional)

If datasource api configured in a such way when api return items only when search is typed, if not - api return empty array. In this case item check became broken, check is not react on click.

It seams that issue related to the DataSource tree load behavior - if search is typed we load items only in visible tree, but checking work based on full tree, which is empty because when search is empty we return empty list.

Steps to Reproduce

1. Open sandbox - https://codesandbox.io/p/sandbox/uui-forked-z4cm8w?file=%2FExample.tsx%3A10%2C42&workspaceId=1dc5a6c7-6fb2-4cae-8ed5-c1bd7e6e64f0
2. Type to search more than 3 symbols
3. Try to check item

Actual result

Item isn't checked

Expected result

Item became checked

Environment

• UUI version: 5.11.0

[cpoftea]

Clone #2565

[AlekseyManetov]

@cpoftea Thank you for your attentiveness.
I will close the previous one since this one contains more details.