The prediction has two parts:

1. "In California, by April 15, 2021, Covid-19 vaccines will be available to all adults" – This is correct. California officially expanded eligibility to everyone 16+ starting April 15, 2021, as announced March 25 and implemented April 15 by the Governor’s office and Cal OES.​(gov.ca.gov)

2. "…and by May 15, 2021, every Californian who wants to be vaccinated will have been able to receive a Covid-19 vaccine dose" – This is not supported by the evidence and is overly optimistic.

   • State projections on March 25 explicitly said that even with expanded supplies it would take several months to vaccinate willing Californians, not one month after April 15.​(gov.ca.gov)
   • By May 4, 2021, Newsom’s office reported that only about 60% of eligible Californians had received at least one dose, and was still rolling out major initiatives (targeted clinics, at‑home vaccinations, free transportation, $85M for community‑based outreach) specifically to reach people who hadn’t yet been vaccinated, especially in hard‑to‑reach communities—i.e., many willing people still had not been served.​(gov.ca.gov)
   • On May 15, 2021, the Los Angeles Times noted that just over 50% of all California residents had received at least one dose, meaning roughly half the state was still unvaccinated at that point.​(latimes.com)
   • Later in 2021, California continued vaccinating millions more people; by late August or December, the state was only then reaching ~80–86% of eligible residents with at least one dose, indicating that the process of vaccinating willing Californians plainly extended well beyond mid‑May.​(gov.ca.gov)

Because a large number of Californians who eventually got vaccinated had not yet received a dose by May 15, and the state itself expected and observed that vaccinating the willing would take several months rather than one, the second (timeline) part of Chamath’s prediction did not come true. Overall, combining both clauses, the prediction is best scored as wrong.