I thought your question had already been answered a few times now.
Maybe I don't understand your question. If there is a part that is unanswered, please ask again.
For this specific project, what is the identifiable benefit to any of the other states or the nation as a whole?
You have not answered.
Transportation is key infrastructure needed by businesses, and thus benefiting GDP. US GDP is an aggregate of the states, of course. Growing our total product is a matter of growing the product of each state. All states benefit from a higher US GDP through interstate trade, federal tax dollars, global competitiveness of the US in general, strength of the dollar, etc., etc. The US gets involved when projects are of a size that is challenging for a single state and where there is benefit from the project being completed.
Businesses demonstrate the need for fast travel between these two cities by the fact that it is the second most used route in the US (LA / NYC being #1). Fast alternatives are rapidly becoming unavailable as they are limited to air travel and the air system in that area is growing toward capacity limits. The possible number of take offs and landings at an airport are not infinite.
Other alternatives to fast rail (such as new airports and runways) are also extremely expensive and have other issues. New freeways are also incredibly expensive and NOT fast. Of course, roadways have other advantages, disadvantages and capacity factors as well.
You can go read the studies on economic impact, etc., if you really want the blow by blow. I'm not going to get into the issue of calculating the exact pay-out date or even how that might be calculated.