Hi again Giacomo,
I recently answered the same question elsewhere, here. To cherrypick and expand upon that for you:
For search engines, the breadcrumbs outputted by The SEO Framework supersede all visual breadcrumbs on your site. With that, the visual ones don’t have a direct effect on search engines, but they can significantly help your visitors nonetheless.
Moreover, this is why you can mostly ignore the breadcrumb issue you’ve explained here, although I don’t know the repercussions.
Google recently dropped its old Search Console, which gave you more insights than the current one on structured data. I do see that they show more active “enhancements” progressively, but breadcrumbs are still absent from this list.
I’ve noticed quite a few errors and discrepancies in the past years in Google’s testing suite; so, take whatever they say with a grain of salt. Only the real search engine results tell the truth.
For fun, this is their newest public testing site: https://search.google.com/test/rich-results
Awesome, thanks once again!