Series is NOT a dublin core (DC) standard.
That said. Calibre will have inserted Non-standard series metadata if it was used in the production (and any conversion where it is now present in the Library) , which any Calibre library will read upon adding. (that is why you sometimes see it right after adding)
Get Metadata:
Various Metadata sites will provide series info. These are not controlled by the Author or Publisher and IMHO are frequently inconsistently recorded and will need massaging to be really useful in grouping by series.
You need to decide on your standards for Series entry
Mystery not Mysteries (almost always,singular in any series. Hardy Boys stays
)
I drop Leading Articles (A, An)
I drop Trailing 'Series" Duoh!
There are various threads on how to index Omnibus Series. Pick one
Manage Series PI
is a great Massager (but not a source. that is up to you to identify)