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Data Table: Set Filter via Callback that is visible in frontend

All,

first of all: A lot of credit to all of you who are commenting here. That I got as far as I got on my own is largely credited to comments here.

Regarding my problem:
I do have a pie chart, that - on click on one of the areas - is filtering the data table via a callback. That works fine. The result is a newly ordered table as expected.
However, I would prefer to show that filter which was applied to the user, so he can choose to remove it or change it easily again.
Actually therefore I would like to use the native filtering of Data Table by inserting (and showing) the filter term, instead of passing on filtered data to the data table.

Is this possible? If so: how?