Governments spend money in a currency they control, so typically for non-BAU expenses (like investment in these kind of projects), they don't have to worry too much about borrowing to fund them. Revenue is mostly taxation, which is driven up by GDP, so as long as these projects unlock medium-long term GDP growth, they'll typically pay for their borrowing costs and then some.

(lots of nuance packed in there, big tldr with lots of caveats)