Are higher-mAh power banks actually delivering their rated capacity?

No, and reviewers are increasingly transparent about this. Real-world output is typically 60–75% of the rated mAh once you account for voltage conversion losses and the battery's own overhead. A 20,000mAh pack labeled at 3.7V cells usually delivers roughly 13,000–15,000mAh worth of usable charge at 5V phone voltage.