For civilian applications, EMC standards and tests primarily ensure the RF leakage is not severe enough to create harmful interference to other devices or users

For civilian applications, EMC standards and tests primarily ensure the RF leakage is not severe enough to create harmful interference to other devices or users of the RF spectrum, and that your device is robust enough to handle reasonable interference from others. But, it's not designed to eliminate information leakage and protect you from enemy actions. There are specialized (often military) EMC standards that are designed to do this, most famously, TEMPEST by the U.S. government. But you're unlikely to see it in any consumer electronics. Heavy shielding is required.