Hello @tkaiser, thank you for provided tips.
I'm still collecting this data, which you have requested and I will add it later.
Also it looks like I managed to find out one of the reason of the issue: It is new version of Silicon Power SSD drive (SP60).
The same issue I've got if try to use Banana Pi M1 with that SSDs, so issue appears not only with M1 + and also with usual M1(I have several such SSDs, so it is not a problem of a particular one).
If I transfer system to the old version of SSD, everything works.
Thanks, Roman.