This makes me sad because I moved to the Bay Area in 2021 and to me Big Basin is just a large burnt out piece of land. I spend a lot of time down there surfing and I don’t think the park has even reopened.
The park is partially reopened last year and you can definitely bike or hike in without reservation (https://www.parks.ca.gov/?page_id=540). My friends and I were able to ride a lot of trails but the shade is mostly gone for sure.
I grew up in the East Bay and was fortunate to have a camping trip there almost every Summer. Some of my earliest outdoor adventures were under, over, and around those giant trees. It really was beautiful.
If you want a similar experience now, your best bet is to head north on 101 into the Redwoods State and National Parks system, visit places like Avenue of the Giants and Women's Club Grove. All north of Garberville. Spots along the road will all be crowded from now through September, but if you do some exploring of your own, you can still find some nice quiet places full of enormous trees.
It is re-opened though not every trail is open. The burn reached highway 1 near Pigeon Point/Ano Nuevo through Big Basin. I rode my bicycle through Butano to China Grade last week and went through 236 earlier this year to Boulder Creek.
I hiked up to the old airstrip in Butano in July 2021 right after the fire. I probably missed seeing the signs saying it was closed. There were lots of still standing redwood trees that looked charred like logs from a fireplace. And then all along the height of the trees there were little green shoots poking out. Still alive.