We do not have any good research backing "bugs found later in the process cost more to fix".
If anything, the few empirical and solid dataset we have show no correlation, to at best really light one.
This principle may sound solid in theory, but the evidence is not here to support it and if anything seems to point to its invalidity.
See in particular https://shape-of-code.com/2021/06/27/increase-in-defect-fixi...