Signs later used to write divine names, including the one that later writes Inanna, do occur in the archaic lists. It is tempting to read that as the goddess attested at the earliest levels, and the temptation should be resisted.
The sign in question is a pictogram of a standard or reed bundle, and in the archaic corpus it appears in administrative and lexical contexts where it may denote an institution, an office, a commodity designation or a place as readily as a deity. What a sign came to mean in the third millennium is not evidence for what it referred to when the earliest monumental buildings at Uruk were raised. Establishing continuity of reference across that interval requires a text that states it, and no such text has been read.
The investigation is therefore open rather than closed. The corpus is still being edited, new joins between fragments continue to appear, and readings improve. What has not appeared is any archaic text naming the recipient of the earliest buildings.
The atlas records the position honestly: the Eanna precinct's later dedication is secure, its earliest dedication is not established, and the oldest writing we have declines to answer the question because it was never asked to. Recording an inconclusive investigation and stating what would resolve it leaves the door open for the tablet that has not yet been read.