Picard currently does not support the Series entity in any way, shape, or form. https://community.metabrainz.org/t/podcast-style-proposal/5911/3 suggests adding podcasts as Series-organised Recordings (which, incidentally, is what I'm already personally doing), but Picard does not currently support doing anything meaningful with this. PICARD-711 also talks about grouping Series of Releases/Release Groups together when tagging them.

FWIW, beets has a ticket for Series support at https://github.com/beetbox/beets/issues/1273