CARTO Builder allows users to edit feature attributes directly from the map building and editing interface.
Does Airship offer the same function?
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As explained in CARTO documentation, Airship is a design framework to build (geospatial) applications. It works nicely with CARTO VL and CARTO JS, but you could add it to any of your projects. Basically, it helps you to apply already designed layouts (sidebars, panels, toolbars...), components (widgets, legends, sliders...), and styles (colors, typography...).
In order to manage your data (edit, create, delete, update...), you should use CARTO's SQL API, Python SDK, CARTOframes or as you said, Builder. You will find plenty of tutorials in their Help Center regarding this topic.
Unfortunately, Airship does not have a editing feature component. You can add a feature request as an issue at https://github.com/cartodb/airship but I am afraid that due to the very limited use case, it won't be taken into account.