From a purely chronological reading order perspective, you’d finish all nine Iron Druid books, then move to 'Ink & Sigil.' There are also short stories and novellas, like 'The Grimoire of the Lamb,' that slot in earlier, but they’re not essential for the series jump. The sequel series doesn’t continue the plot threads from 'Scourged' in a linear way. Instead, it shows the ripple effects.
The magic system, especially the dealings with gods and fae, remains the consistent thread. Hearne uses the sequel to delve into a different corner of his cosmology, one that was always there but never the focus. It’s a satisfying expansion for lore enthusiasts.