North Philly library branches are embracing a new, modern role: filling the gap left by rec centers.   As a 21-year-old mother of three, Mieka Moody arrived at Central Library to take a library assistant exam practically by chance. “When I was a child, I did not say I wanted to be a librarian,” Moody says. “Actually, I did not even spend a lot of time in libraries.” Among the crowd of 100 or so test-takers was her mother, who had been studying for weeks. The results came in and her mother didn’t make the cut. Moody did. Now, Moody is the branch manager and sole librarian of the Lillian…