Certainly not very urgent / important, but it came up. Currently there is no overall (summarizing) test statistic for the CUSUMSQ analysis.
This reference looks relevant: https://doi.org/10.1017/S026646660808033X
(Deng & Perron 2008) It seems to have some max() formulations in it, i.e. it seems to boil down the sequence to a single statistic.