Just because a University receives some public funding for its operations, does not make it a “publicly funded art gallery” or “a publicly funded archive that collects and displays artworks”. Universities receive funds and revenue from many sources. Any artworks the University has collected and displayed may have been purchased other than with public funds (e.g. through University operating revenue, sales of assets, or private bequeathments or foundations). The proportion of public funding it does receive is likely to be ear-marked and attached to tuition, rather than for the purpose of operating an art gallery or archive to collect and display artworks.
Universities may establish special bodies to collect and display artwork. But unless that special body is in effect operating as an art gallery or archive (etc) that collects and displays artworks, and its operation is publicly funded (e.g. it applies for and receives public funding for that purpose) then resales involving that body are unlikely to automatically qualify as a professional resale (unless an AMP or GLAM is involved in the resale).