False. The federal government does not pay for anything; it forcibly transfers money from some people to other people.
What Biden really means is "look how caring I am in making all Americans pay, rather than just the people of Baltimore, or the people of Maryland, or the future users of the bridge."
Not that I'm particularly bothered. We're forced to pay for all kinds of infrastructure projects. But we should make a habit of looking beyond the superficial claims to understand who really pays and why.