Seagate has introduced the Exos M series, a range of enterprise-grade mechanical hard drives available in 30TB and 32TB capacities. The two models, the 30TB CMR ST30000NM004K and the 32TB SMR ST32000NM003K, each offer a minimum of 3TB per disk and use a standard 3.
Raspberry Pi or an old office PC are the usual methods. It’s not so much programming as Linux sysadmin skills.
Beyond that, you might consider OwnCloud for an app-like experience, or just Samba if all you want is local network files.