In the US, if one had no "income" other than, say, $1,000,000 in long-term capital gains, how would that be taxed?

Capital gains are included in "total taxable income" when working through the worksheets to determine the tax rate. They are not ordinary income that is calculated using the brackets for ordinary income, but they are taxable income.

So yes, you would calculate the long-term capital gains rate using $1m of "taxable" income. The first $47k of gains would be taxed at 0% (since you had no ordinary income to use up that bracket), the next $472K would be taxed at 15%, and the final $481k would be taxed at 20%.

NerdWallet (not an endorsement) has a good calculator that splits out the gains into each bracket.

There might be other taxes involved, but the main point is that capital gains are included when determining the bracket to use for the marginal rates