Answer
This has been confirmed as a real limitation specifically for multi-select custom enumerations — searching/filtering on a collection-type element like this isn't supported at all, regardless of the Searchable setting; attempting to force it (for example, via the main advanced search) returns an explicit error rather than a working filter. A single-select custom enumeration or plain text attribute doesn't have this restriction, so if filtering on the field is a requirement, a single-select design (or a different attribute type entirely) is needed rather than a multi-select enumeration.