You create the filter as required.
You create a window and add the filter as a tab.
You then create the correct window publishing rule that ensures your end users see the window with the filter on, and not the one the analysts see.
(You don't need to apply the filter at the object level - ie on the Notes attribute within Incident - you add it to the window you publish instead)
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Have you worked through the documentation and community articles about how to set criteria on filters?