If a mainland passport returns to Hong Kong via Taipei from New York, do I need a Taiwan entry permit to transit at the same terminal?

No connecting flights. If the non-connecting flight does not leave the customs, please ask the airline company of the next route, maybe their staff can pick you up. If you go out of the customs, you must have a Taiwan Entry Permit and a Chase Pass.

unnecessary. . . . . . .

You don't need to go out of the customs, you only need to stay here.