The Seychelles is still 40% unvaccinated. Even people who are vaccinated have some chance of getting infected, though if they get infected, their chance of showing symptoms is lower, and their chance of ending up in the hospital is much lower. It looks like the people testing positive in the Seychelles are mostly unvaccinated, and that the people ending up in the hospital are even more likely to be unvaccinated. But there's not enough information in the BBC article to judge just how effective the vaccines have been in the Seychelles.
The BBC article does contain one falsehood:
> In April, China's top disease control official said the efficacy of the country's Covid vaccines was low, although he later insisted his comments had been misinterpreted.
George Gao did not say this. He gave a talk at a conference on vaccines which was blatantly misconstrued by a "researcher" at an American think tank, the Council on Foreign Relations. That misrepresentation then got spread by the media. All George Gao actually said was that researchers should consider ways of increasing the efficacy of vaccines that have lower efficacy. He didn't name any specific vaccine or any specific country. He proposed the same sorts of measures that are being considered for other vaccines, such as the AstraZeneca shot: delaying the second dose, mixing vaccine doses, etc. This got twisted into an "admission" that Chinese vaccines have low efficacy. It's too bad to see that the BBC is still repeating this false claim, weeks later.