"Quick Find views are used for configuring Dataverse search, so you can manage global search, quick find, and lookup search behavior in one single place". (Configure Dataverse search to improve search results and performance - Power Platform | Microsoft Learn, 1010.2022)

Operators are available for Global Search (Search for tables and rows by using Dataverse search - Power Apps | Microsoft Learn, 10.10.2022) but not for Quick Find (Quick Find - Power Apps | Microsoft Learn, 10.10.2022)

The difference between Global Search and Table(formerly Entity) based 'Quick Find' --> 'filter this view' is that the latter would require to add a leading asterisk. This, however, is a bit confusing to end users (they don't understand it at all!).

• When do I need to add a leading asterisk to search 'contains'?
• Why can't I add operators such as 'Contoso | Testfabrick" to Quick Find`?

At the bottom line: for a consistent UX, I would prefer to have 'fiter this view' be subject of data verse serarch but limited by the view specific conditions.