Russia has good designs.Russia stopped building big ships, while China was only getting started, and older ships can only last you for so long before they need to be scrapped. In the future Russia should just buy destroyers and size up ships from China instead.
Student has indeed became the master.
For example, their Admiral Gorshkov FFG is a GREAT design and they have built one and are ready to launch a second.
The Admiral Grigorovich FFGs are a very decent design as well (they have for or more of those now:
Other than that...they have built quite a few new Corvettes that are very decent aas well...probably more capable than the Type 056.
But the problem Russia has is money and budget...and then, since it has been going on such a long time, their industrial capability is slacking too because the people who used to do that, and then train new people as they came along, have all retired. (Maybe not all, but enough to have hurt them)
So, they are not able to build as many ships as quickly as they once did, and they are falling way behind the US and China in terms of capacity and numbers.
They will continue building their own designs. I do not expect to live long enough to see the Russians buying new ships from the Chinese. The Chinese did it as a stop gap...and it is costly to do because there are all sorts of language and logistical problems with spare parts and maintenance.
China did it though and then has enough money now to completely refit those ships into a form that is more modern and better for China because they are putting Chinese systems on those ships now, and they can build everything they need to do do so.
Russia will not want to go down that road...and I expect that they will wait a long time to do so even of they had to.