How can I use/get newspapers on microfilm if Berkeley owns only non-circulating master and archival negatives?

This microfilm does not circulate, since Berkeley is only acting as a storage place for the archival copies. UC Berkeley does have another copy of some of titles, and records for these will appear in OskiCat

All of the California newspapers of this kind have circulating microfilm  housed at the California State Library in Sacramento. While these copies do not appear in OskiCat, they do appear in the Melvyl catalog.

If you are a UC Berkeley faculty, student, or staff member, you can request the film through Interlibrary Borrowing. If you are not affiliated with UC Berkeley, you can use the material at the California State Library or request it through your local library's Interlibrary Borrowing office.