NEW YORK — The failure of President Joe Biden’s ambitious “Build Back Better” funding bill last December also had another casualty — nearly $3 billion meant to plug a looming deficit in the World Trade Center Health Program. Now lawmakers are searching for a new way to advance legislation to fill that hole after a recent briefing to lawmakers by 9/11 health program staff, the Daily News has learned. If the Build Back Better legislation had passed, it would have forestalled what could be a grim outlook for the health program and its 117,000 members, and the possibility that the program would ha…