I've never heard of nor seen "Nobility Books".
In 1785 Catherine II issued a Charter for the Rights, Freedoms and Privileges of the Russian Nobility. See
full text here. Its section 3 dealt with the keeping of genealogical records. The Russian Wikipedia says:
Составление дворянских родословных книг
Уездные предводители осуществляли составление родословных книг. Все потомственные дворяне обладали равными правами независимо от разницы в титулах и древности рода. В Родословные книги вносились только потомственные дворяне, личные дворяне в них не вносились.
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Compilation of noble genealogical books.
Marshalls of the nobility of each uyezd carried out the compilation of genealogical books. All hereditary nobles had equal rights, regardless of the difference in titles and antiquity of the genus. Only hereditary nobles were entered into the genealogical books; personal nobles were not entered into them.
Russian noble families were thus recorded in "nobility books" in the governorates where their main estates were located. These records were important, as they were the census for participation in the provincial assemblies of the nobility, an aristocratic form of local government.
But I can't see how there could be a 6th book of this type, as they were geographical. All noble, armorial families were also listed in the General Armorial of the Noble Families of the Russian Empire (see
https://gerbovnik.ru/), which had different sections and volumes, but essentially was one huge comilation. I can't find the Birons at all there.
Remember that the von Bührens / Birons were not Russian nobility per se, and neither part of the original
Ritterschaft, the German knightly estate, of Courland, but had been ennobled by a King of Poland. Though I would presume they would be listed in different Russian provincial nobility books if they had estates in those governorates.