I am in agreement with all of this. The Search widget in Experience Builder needs to mirror the capabilities in WAB. For those wanting to search layers in a the web map used in your Experience, you CAN configure a search through the settings tab in the Item Details page of your web map. Under Application Settings, toggle on By Layer and configure your search there. It's not a complete fix to the shortcomings of the Search widget in Experience Builder, but it does provide some functionality.
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