Since the returns will be paper filed, no point in using the estate bank account because paper checks will be issued anyway (no direct deposit). There must be an EIN because a bank account couldn't be opened without a TIN. It doesn't go on the 1040 unless there is income paid after the death but reported to the decedent. For example, a brokerage account may report the whole year worth of dividends to the decedent, in which case you put the whole amount on the 1040 and then back out the amount paid after death, using the explanation "IRD to be reported by EIN...." That won't be an issue until 2023.
Don't worry about confusing CT or IRS. IRS doesn't pay much attention to state entries, and CT won't complain if you report income to them.