@mib2berlin It was quite difficult, but I managed.
Firstly, thanks to "Trigger getUpdates", another Yandex button has appeared in the mobile version, but it is still outdated. The icon was updated only after the replacement "yandex.ru" to "ya.ru ".
Secondly, Vivaldi on Android has pre-installed search engines, which for some reason do not sync with the desktop version, so it is impossible to delete them (for example, go.mail.ru ). The solution turned out to be to manually add the same engines in the desktop version (after forced synchronization in the desktop Vivaldi, these engines were duplicated), and then delete them and their duplicates. It looks like a bug, this shouldn't happen
But after all the manipulations, I achieved the desired result, thank you!