BUDAPEST—Hungary’s capital city is offering free antibody testing to its elderly residents in a bid to ratchet up pressure on the government over concerns that certain vaccines don’t provide adequate protection against the coronavirus. The offer of 20,000 free tests, available for Budapest residents over 60, came after many fully vaccinated people reported that tests they had undergone at private laboratories indicated that they hadn’t developed antibodies to defend against COVID-19. Budapest Deputy Mayor Ambrus Kiss said those reports came primarily from people who received China’s Sinopharm vaccine, convincing city leaders that there was “a genuine problem.” He said the government should consider offering third doses to those with inadequate immune response. “If there is such a loss of confidence in certain vaccines, then the government needs to order a third dose and free up the capacities for giving them,” Kiss told The Associated Press, adding that the tests are …