You are correct, and it looks like I spoke in error. Here is what the TreasuryDirect website says:
I bonds increase in value on the first day of each month, and interest is compounded semiannually based on each I bond’s issue date. An I bond’s issue date is the month and year in which full payment for the bond is received.
But today’s 7.12% interest won’t compound for the rest of the life of the bond. However, it looks like the subsequent 6-month rate will be added to the compounded increase at the end of the first 6 months — an even better deal than I thought!