Adding to the suggestion from @Kellen, I had to ask a new question to figure out exactly how to access this state as it is not exposed via the api. The answer is here https://stackoverflow.com/a/79315889/9625 (Thanks to @MrOnlineCoder)

For completeness I am posting the the code-snippet in case anyone finds this question via Google as I did.

<p-datatable :value="customers" :filters="customerFilters" ref="datatable">
  ...
</p-datatable>

...

const datatable = useTemplateRef('datatable');

...

let filteredCustomers = datatable.value.processedData  
let str = "Customers in filter: "
str += filteredCustomers.map(customer => customer.fullname).join();
alert(str)