Russia claims they've solved it already and, according to the FSB . . . drum roll . . . it was a Ukrainian:
>>>In its statement, the F.S.B. alleged that a Ukrainian woman had been contracted to carry out the bombing, saying that she had entered Russia on July 23 and rented an apartment in the Moscow building where Ms. Dugina lived “in order to organize the murder of Dugina and obtain information about her lifestyle.” The woman was at the same nationalist festival attended by Ms. Dugina and her father on Saturday before the bombing, the agency said. . . .
But the F.S.B. statement may be unlikely to convince critics of Mr. Putin that Ukraine was indeed behind the crime. Coming just over 36 hours after the blast, the agency’s declaration that it had “solved” the crime represented an extraordinarily rapid investigation compared to
other high-profile assassinations — like those of the opposition leader
Boris Nemtsov in 2015 or of the independent journalist
Anna Politkovskaya in 2006, cases that remain unsolved. <<<
https://www.nytimes.com/live/2022/08/22/world/ukraine-russia-war-news
The Ukrainian government would have almost nothing to gain by killing Daria, and they'd have plenty to lose. I really can't imagine any government would want to do it.
There's been speculation that Putin ordered the bombing in retaliation for Dugin criticizing Putin's handling of the war in Ukraine. Putin has certainly shown that he will not hesitate to kill people who cause problems for him, but I'm not sure this is the answer.
It would be awkward for the FSB to pin it on an internal group in Russia because this would show domestic weakness, but it is also somewhat awkward to pin it on Ukraine because this shows weakness with regards to security against Ukraine infiltration.
I'd guess there are militants in the middle east who resent Russia's military interventions there, but it seems like it would be difficult for them to pull this off.
It's not clear what entity would have both the motivation and the capability to do it.