I.e. for every $1 that NY sends to the federal government in federal taxes, it receives something like ~$0.80 in spending: https://www.osc.state.ny.us/press/releases/oct17/100317.htm. Most of the money that NY receives is for Medicaid and other entitlements.
NY receives every year a total of $165 per capita for transit, slightly less than the national average of $168. When considering the cost of labor and materials in NY, that gap is probably much larger in real purchasing terms.
On the other hand, NY state directly spends $639.2 per capita on transportation annually: https://www.usgovernmentspending.com/year_spending_2019NYdn_.... The actual cost of the "pensions" you deride is $1085.2 per capita per year to the state. If you look at total state and local spending, the total costs of pensions are $1758 per capita per year, and transportation is $1788.8 per year. Neither reaches 10% of total statewide spending.
This doesn't directly negate your point about federal money trickling down, but NY is not receiving very meaningful assistance from the federal government.