The IBX is a new rapid transit line planned in Brooklyn and Queens. Here is the most recent context I've seen for its price and timeline.

"The cost and the timeline for the project is still unknown, though MTA Chairman and CEO Janno Lieber previously estimated the entire thing would take between three and five years, and cost in the “single-digit billions” (which is a wide range between $1,000,000,000 and $9,999,999,999 — though the light rail is more affordable than the conventional rail option)." from https://nyc.streetsblog.org/2023/01/10/hochul-gives-green-signal-to-light-rail-on-the-interborough-express/

See official project page here: https://new.mta.info/project/interborough-express