using LUCID key to plants of SouthEast Australia takes me to Calandrinia pickeringii. This isn't on CNM or in the Census but the fit is good. ALA shows one record for Canberra, and one from the Shoalhaven.
The source below suggests that "Identification to species level of Calandrinia usua ly requires microscopic examination of the seeds." https://apps.lucidcentral.org/plants_se_nsw/pdf/entities/calandrinia_pickeringii.pdf
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