Ultimately, I took the advice from one of the comments, and just queried the HTML of the page.

// Directly check for the existence of .ag-filter-wrapper
const filterDialog = document.querySelector(".ag-filter-wrapper");
if (filterDialog) {
  console.log("Filter dialog is open, delaying data reload.");
  return;
}

This accomplished what I needed, which was halting my update routine if the filter was still open.