I want to filter a large library in SharePoint Online using columns headers filters on managed metadata fields. I know it's also possible to use Managed Metadata Navigation in classic mode, but users like filter on column headers because of less clicks needed. So if they use columns headers filter, does it have throttling limits or is it search based?
Whatever ways (indexing, filtering, folders, and offline data) you're using, they all have throttling limits.
In general, Indexes work with filters.
If the number of items in your list or library exceeds the List View Threshold, but are still under 20,000 items, you can usually add indexes to existing columns. You can then apply filters to get the displayed data under the List view Threshold of 5000 items.