I guess by not checking the "Use also for old translations created with the classic editor" checkbox, the translations made with the legacy translation editor should still be editable (via this legacy editor), but even on these cases, the translations are loaded trough the new advanced editor (e.ate.wpml.org).
Older posts date back to 2021, when I think there wasn't an advanced editor available.
I’ve taken and deployed a copy of your website, but I’m having trouble reproducing the issue you described.
For example, I checked Project > Protocol abordatge ..., and when I click that post, it opens correctly in the ATE editor and is fully translated there, which mean they used ATE editor and where translated there.
So I’m not sure which posts you’re referring to when you say they were created in the CTE (legacy) editor but now open in the ATE (new) editor with empty translations. Could you please share a few examples?