I think what you are looking for is Literary Naturalism. This began as a reaction to the prevailing modes of surrealism and Romanticism of the period (late nineteenth-century) and was an off-shoot and more advanced form of realism. As such is it often called 'extreme' realism and is somewhat synonymous with the effects of realism; it depicts events and other objects as they are, often to the degree of being judged unnecessary.
(As a side effect, determinism is usually (although not absolutely) associated with Naturalism, and uses pessimistic realism to determine an unchangeable outcome of a character's life, usually tragedy, which explains why many of Tolstoy's works do not end happily. This however is not about inconsequential details and acts on a much larger scale to the narrative.)
This technique was primarily employed by Emile Zola and many American authors, including Edith Wharton in her novel The House of Mirth, which I will use here as an example for the technique, where she details everyday items inconsequentially:
when it came to hunting for
missing napkins, or helping to decide whether the backstairs needed
re-carpeting, Grace's judgment was certainly sounder than Lily's: not to
mention the fact that the latter resented the smell of beeswax and brown
soap, and behaved as though she thought a house ought to keep clean of
itself, without extraneous assistance.
The napkins, carpet and the smell of beeswax and soap contribute nothing effectual to the narrative apart from injecting an extra sense of realism.
In terms of Russian literature, Tolstoy was know to use it in his novel The Death of Ivan Ilyitch (especially in Ilyitch's eventual anti-climactic death from a fall whilst hanging up curtains).
Sometimes he even had moments of absent-mindedness during the court sessions and would consider whether he should have straight or curved cornices for his curtains. He was so interested in it all that he often did things himself, rearranging the furniture, or rehanging the curtains. Once when mounting a step- ladder to show the upholsterer, who did not understand, how he wanted the hangings draped, he mad a false step and slipped, but being a strong and agile man he clung on and only knocked his side against the knob of the window frame.
Here, the cornices distract Ilyitch during court sessions but do not create much impact in themselves apart from being realistic, since people do, after all, remember little unrelated details.
Furthermore, the way his deterioration drags on is also reminiscent of the realism of Naturalism as the insignificant details seem to prioritise the content of the narrative. Overall, the whole story is about the realistic qualities of an ordinary man's inconsequential life and so Naturalism is a necessity in achieving this effect.
Likewise, Anna Karenina also features Naturalistic descriptions:
When he was dressed, Stepan Arkadyevitch sprinkled some scent on himself, pulled down his shirt-cuffs, distributed into his pockets his cigarettes, pocketbook, matches, and watch with its double chain and seals, and shaking out his handkerchief, feeling himself clean, fragrant, healthy, and physically at ease, in spite of his unhappiness, he walked with a slight swing on each leg into the dining-room, where coffee was already waiting for him, and beside the coffee, letters and papers from the office.
It is evident here that the overwhelmingly list-like details appear to be redundant, however it really does paint a solid realist picture of the presented scene.
This page explains Tolstoy's tendencies to realism if you are specifically after his use of Naturalism/realism.