One of the pandemic tax changes of the last year has been to make the Child Tax Credit fully refundable IF you and the child spent a majority of the last year living in the US. See question #10 at this IRS website.
Your situation does open up some interesting possibilities, but I would depend only on the numbers of the tax forms themselves.
Sometimes these summary pages (like Your Tax Breaks) show numbers that don't actually match what's on the return - not because they're wrong, but because the summaries are showing the total amount you entered and not the amount that ends up on the tax return.
As for credit rollovers, that varies from credit to credit. Some credits can be carried forward and some can't. Sometimes, if a credit is limited and amount would be carried forward, there could be a message in the TurboTax input screen at the time, but I don't know of a single place where you can see this for all credits.
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