Is this a spike compared to last few months? Where is best place to get the latest chart of unemployment over time for 2020?
The latest jobs report, which has a graph of the year's data, is here: https://www.dol.gov/ui/data.pdf
The numbers here are basically on an exponential decay curve from ~6M new claims in the last week of March. (FWIW, the pre-2020 record for new weekly claims, seasonally adjusted, was ~700k in 1982--we broke that in March and haven't stopped breaking it since).
They release a jobs report on the first friday of each month with asjustements as data from prior months made it in. They survey businesses and process a lot of other data to deliver these reports and have been generally apolitical and data focused though the current administration has tried to influence numbers to their advantage, effectively undermining a critical component of our democracy.