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Metadata and Custom Metadata Types Support
LWC Offline uses the UI-API to access standard metadata.
Metadata for entities, layouts and other customizations, and Lightning web components is automatically primed or loaded when used, and is cached for offline use. However, the UI-API doesn’t support loading custom metadata types. As a consequence, custom metadata isn’t primed or cached automatically. This affects features that use custom metadata, such as Flows.
If you must retrieve custom metadata, you can do that using Apex requests. If your Apex request methods are cacheable, the custom metadata you access is available while offline. See Use Apex While Mobile and Offline.