Accounts such as retirement accounts or transfer-on-death accounts that have beneficiaries other than the decedents estate are not your responsibility as executor other than to inform the financial institution(s) of the death and to provide a death certificate. Such accounts become maintained for the benefit of the designated beneficiaries immediately upon the death of the account owner, so the beneficiaries are responsible for the taxes on any post-death income in the account. These accounts are not part of the probate estate. The only effect they have with respect to the decedent's estate is the amount they add to the gross estate when determining if the estate is subject to federal or state estate taxes.
A delay in informing the financial institution could result in the financial institution issuing Forms 1099 to the estate for post-death income when these forms really should go the the account beneficiaries. This might necessitate using the nominee process to forward these forms to the beneficiaries.
Accounts that have the estate as beneficiary, possibly by default if no beneficiary is designated, would be your concern as executor until liquidated by the estate or distributed out of the estate subject to the terms of the will.
It's not clear why you would be receiving any account statements for accounts that have designated beneficiaries where you have informed the financial institution of the death. The financial institution should be dealing with the account beneficiaries.
