Is this park a state park?

No

It is not a state park., but a huge one with a lot of museum (De Young Museum, Academy of Science, Conservatory of flowers....), and gardens (Japanese tea Garden, Botanical Garden.. .) to visit. It worth it

Yes

Large park. Good greenery. Free to public

So worth a visit. We spent 2 days in there and there was more to see

As everyone said: no, its not a staye park. But its huge and gorgeous and full of museums and gardens and lakes and playgrounds and wildlife

No it's a large city park that is free to walk around in and cost nothing to enter