Yes, the exclusion is automatically added when you open your amended return. If you qualify the unemployment exclusion is deducted on line 8 of Schedule 1.
If your modified adjusted gross income (MAGI) is less than $150,000, then you can exclude up to $10,200 of unemployment compensation paid in 2020 from your taxable income. Amounts over $10,200 for each individual are still taxable.
No, you do not wait for a new 1099-G.