I've seen (somewhat) conflicting claims. Wikipedia claims it's officially part of the National Guard of Russia since 2023. For this it cites the Russian [expat] opposition website Meduza. But that piece doesn't quite seem back up the claim. Instead it says something more complicated (in Google translation):
A PMC recruiter told Important Stories that he represented “the only unit that has an official contract with the Russian National Guard.” According to the publication, the negotiations on the mercenaries’ transfer to the Russian National Guard were conducted by Pavel Prigozhin and the Wagner PMC commander Anton (Lotus) Elizarov.
On October 17, the State Duma adopted in the first reading a bill allowing the Russian National Guard to create "volunteer formations." The media assumed that mercenaries from the Wagner PMC could join the Russian National Guard's "volunteer formations." One of the authors of the bill, deputy Alexander Khinshtein, claimed that the document "has nothing in common" with the information about the transfer of former Wagner PMC units to the Russian National Guard.
OTOH, the BBC claims, citing an [apparent] expert that
According to Dr Watling, "there was a meeting in the Kremlin fairly shortly after Prigozhin's mutiny, in which it was decided that Wagner's Africa operations would fall directly under the control of Russian military intelligence, the GRU".
Control was to be handed to Gen Andrey Averyanov, head of Unit 29155, a secretive operation specialising in targeting killings and destabilising foreign governments.
In early September, accompanied by deputy Defence Minister Yunus-Bek Yevkurov, Gen Averyanov began a tour of former Wagner operations in Africa.
Al-Jazeera makes somewhat similar claims, but they also suggest a split (at least naming-wise) between the Russia+Ukraine branch and the rest:
Command of Wagner’s overseas presence has been assigned to Russia’s military intelligence (GRU), specifically General Andrei Averyanov. Through a series of intermediate PMCs like Convoy, established in Russian-occupied Crimea in 2022, and Redut, active in Ukraine, but established in 2008 to protect Russian commercial interests, maintaining legal deniability, Wagner’s Ukrainian operation is being retitled the Volunteer Corps, with other operations becoming the Expeditionary Corps.
Another source (the Institute for Security Studies--which seems to have US and South Africa offices) says
The Russian military company Wagner appears to have been renamed the Africa Corps by Moscow, and brought under the control of Russia’s Defence Ministry.
But they MSN piece they link for that seems again to partly contradict what's claimed:
The Africa Corps consists of mercenaries and volunteers, and does not form part of the Russian Armed Forces.
So, whom or what does Wagner (or whatever it was renamed to) belong to--officially--if [to] anything?