As of my last knowledge update in September 2021, coelacanths were considered a vulnerable species, but they were not classified as critically endangered. Their population was limited, and they faced various threats, including accidental bycatch in fishing operations, habitat degradation, and potential impacts from deep-sea mining.
However, the status of coelacanths may have evolved since then, and I recommend checking with more recent sources, such as the International Union for Conservation of Nature (IUCN) Red List or relevant conservation organizations, for the most up-to-date information on the conservation status of coelacanths. Conservation efforts have been in place to protect and study these ancient fish, so it's possible that their status has changed.