I've watched loads of Star Trek stuff over the years but couldn't tell you about much of it off the top of my head (certainly I couldn't tell you shit about the plot of Nemesis or any of the JJ films). I watched the first episode of Picard last night and it was totally fine.
I wouldn't say that there's a lot that you won't understand at all in it if you have a passing familiarity of Trek.
I would say that there is a lot of nuance and subtleties that you would miss if you are not more familiar with Trek.
They're very clearly touching on and building from themes that they've touched on before. Lal, B4, Bruce Maddox, Daystrom Institute.
Then just things like the TNG poker games, the Picard vineyard, Data's paintings, history of the Romulans and The Federation, the Borg etc.
Feels to me like skipping straight to Picard would be like flicking through the first half of a book and starting half way through.