How did the government raise money to pay the war debts

Historically? They either issue new bills (increase the size of the money supply) or make new bonds (increase the size of the federal debt).

In neither case is money "raised," it's simply incurred and then paid for later somehow.

In World War II, war bonds were marketed and sold specifically to US residents, encouraging people to lend their personal savings to the government in return for having the money paid back with some small interest after the war was over.

Today, it's usually done with T-Bills, sold to other governments or very, very large investors, just like every other thing the government wants to finance. It is not kept as a separate revenue stream (or promoted to the citizenry as a patriotic potential contribution).