Breadcrumbs: What specification does Google and Yandex use?

Question

HTML

I checked in the output which specifications work and which do not.
For some reason schema.org is not working! The question is why?
On some sites, I noticed only data-vocabulary working.
Time to switch to it or to what?
PS. But even their website does not work (data-vocabulary.org).
Upd. 90% - data-vocabulary.org, 10% - breadcrumbs without markup, but everything works (mostly in Google).

Answer 1

I asked a question to Yandex technical support and received the following answer:

Any special markup is not taken into account by our algorithms when building navigation chains. Such links are generated automatically; you cannot specify or change them manually. You can only contribute to their correct formation by following our recommendations:
https://yandex.ru/support/webmaster/search-results...
https://yandex.ru/support/webmaster/search-results...
(the principle of formation navigation chains is similar to the principle of forming quick links).
When forming navigation chains, the structure of the site is taken into account first of all. Moreover, over time, such links may appear, disappear or change depending on the changes made on the site.
Among the factors positively influencing the determination of navigation chains, the following can be distinguished:
- the main sections and pages should be accessible from the main page of the site;
- site navigation should be simple and clear;
- page titles should be short and accurately reflect their content;
- the text in the title tag must match the text of links pointing to this page.
I would like to draw your attention to the fact that these are the main, but not all, factors influencing the formation of navigation chains.

PPC, in short, the fate of quick links is the same, sorry ...
The question remains, why is almost 100% a data-vocabulary specification? I don't believe it's accidental. They probably just haven't covered it yet.