In the existing business create payment transaction from Capital account (equity).
In the new business you would record a starting balance in the bank account.
No, you should record a receipt in the new business and not use starting balances in cash or bank accounts. The new business did not exist before. So it is not being migrated.
This situation can be very complex and requires professional accounting advice.
I agree that you should seek professional accounting advice and if you require help implementing that advice into Manager make a further request based on that advice.