As formula columns allow using Python3’s eval, there is a way to have an advanced search widget on a page. This workaround would allow, for example, use cases as Create AND filter or Save filters on table.
As it’s easier to show than to describe, here is a link to a page making use of it. The idea is to define a “filtering table”, with a formula column used as a selector for the table one wants to filter. This formula columns calls eval on a condition column, itself defined as Text, but containing Python code.
While eval, in itself, can easily become an open door to security concerns, the fact that the condition column can only return True/False values avoids most of them.