The main requirement with a conflict of interest is that it must be disclosed to the editors.
Reviews aren't processed automatically, but by an editor. The editor is supposed to read your review - in particular if you indicate a conflict of interest - and may then decide whether your review is fair, or may need to be ignored.
So just do a very thorough review (in your case, probably a very much critically thinking review, because this is also a chance to reconsider foundations for your own work!) and in the confidential remarks, repeat your conflicts.
I have also reviewed papers where I had prior collaboration with one of the authors. It turned out the other reviewers liked the paper, but I found flaws in the proofs. My review "won", they had to fix the proof to get it accepted. Sometimes, a reviewer with a conflict may be the most valuable, because he puts much more effort into the review. The editors just need to know and pay attention to potential bias.
Personally, I would not do the review because you are already working on a follow-up and seem to be quite close to the authors. This most likely makes you too "blind" for the actual problems of the approach. And in the worst case, imagine that you find a fatal flaw when doing the review, which may even kill your own current work? Imagine you find some weaknesses, they need to resubmit, and your own work cannot get published until theirs is, so you end up delaying your own work... so by doing a good review, you may hurt your own research? It's probably better to have someone else do the review - or they missed some weakness, or if they delay publication, neither is your fault. Also, will you be able to remain anonymous to the authors? Imagine you find a weakness, and 'kill' their submission, and you somehow give away you reviewed... will they take this well?