There will be an IRS portal to update your information for the child tax credit. If you do not get the monthly payments you should be able to get the credit on your 2021 tax return. There is nothing to add to your TurboTax "stuff" until you prepare your 2021 return.
Your biological children only count as dependents for the child tax credit and for possible stimulus credits if they lived in your home more than half the nights of the year. If they lived in the home of the other biological parent more than half the nights of the year, that biological parent gets to claim them as dependents, even if that biological parent has passed away in 2021. Their personal representative or executor must file a final tax return in their name to report any income they earned while they were alive, and that tax return will claim the children as dependents if the children lived with that parent more than half the year.
The IRS does not rely on such concepts as 50-50 custody or court orders, the IRS relies only on where the children physically lived. However, you would get credit for any nights the children lived in your home during a custody sharing arrangement. For example, if you got custody on August 1, that’s about 153 days till the end of the year. Half the year is 183 days. You would need to show that the children lived in your home for 30 more days. This might be weekends or vacations during the first half of the year if you were sharing custody under a court order or other arrangement.
If you can’t add up your custody time to 183 or more nights, you can’t claim the children as “qualifying child“ dependents and they will not qualify for the advanced child tax credit. If neither you nor the other parent has 183 days of custody time, such as because the children were briefly in foster care, then no one can claim the children as “qualifying child“ dependents. You can claim the children as “qualifying relative“ dependents if you provided more than 50% of their total financial support over the year. However, a qualifying relative dependent only gives you a $500 tax credit, does not give you the enhanced child credit, the advanced payment of the child credit, or a stimulus rebate.