I found the delay puzzling too. But the NYT obit does link to https://www.colinmcginn.net/john-searle/ near the end.

The Times in the UK publishes obituaries of very well-known public figures within a day or two. Notable but lesser known people (such as Searle) await a quiet day and it can take as long as six months. Space is the constraint, not the availability of the obituary. I guess the NYT is the same.