The £200 is not really a loan to each household where the household must pay it back. The best way to look at it is that all electricity bills will be reduced by £200 in October 2022. From April 2023, all electricity bills will be increased by £40 a year for five years. The government is lending the money to the energy companies who will have to pay back what they borrow.
Somebody who gets a house for the first time after April 2023 will not benefit from the £200 discount, but will still have to pay the extra £40 on their bills each year up to and including April 2027
Somebody who stops being an electricity consumer in March 2023 (dies, emigrates, moves in with someone else etc.) will benefit from the £200 reduction but will never be subject to the £40/year extra.
It doesn't matter whether you move house, change energy suppliers, change the name on the bills, the system will take care of it.
As far as I know the system applies to England only, and the other home nations will be given money and can make their own decisions about their own schemes.