Looking to your question and your comment on the answer of Jakub Kania, would I say that part of the solution is that you will create an extra table.
The issue is that constraints on columns should only apply the functioning of the column itself, it should not affect the values of other columns in the table. Specifying which columns should influence the status 'lastUpdate' is imo business logic.
The idea which columns should have impact on the value of the status column 'lastUpdate' changes along with the business, not with the table design. Therefor should the solution imo consist of a table in combination with a trigger.
I would add a table with a column for a list of columns (column can be of type array) that can be used in a trigger on the table like described by Jakub Kania. If the default behaviour should be that a new column has to change the value of the column 'lastUpdate', then would I create the trigger so that it only lists names of columns that do not change the value of 'lastUpdate'. If the default behaviour is to not change the value of the column 'lastUpdate',then would I advise you to add the name of the column to the list of columns in case the members in the list would change the value of the column 'lastUpdate'.
If the table column is within the list of columns then should it update the field lastUpdate.