WASHINGTON — The Biden administration’s embattled plan to dispense COVID-19 booster shots to most Americans faced its first major hurdle Friday as a government advisory panel met to decide whether to endorse extra doses of the Pfizer vaccine. Scientists inside and outside the government have been divided in recent days over the need for boosters and who should get them, and the World Health Organization has strongly objected to rich nations giving a third round of shots when poor countries don’t have enough vaccine for their first. The panel, made up of outside experts who advise the Food and Drug Administration, weighed a less than clear-cut case: While research suggests immunity levels in those who have been vaccinated wane over time and boosters can reverse that, the Pfizer vaccine is still highly protective against severe illness and death, even amid the spread of the highly contagious delta variant. The FDA experts were scheduled to vote on one basic question: Does the evidence show that a Pfizer booster would be safe and effective for people 16 and older?