At least for LPR they now becoming part of Armed Forces of Russia, as can be read in this Russian article:
The People's Militia of the LPR may become part of the Armed Forces of Russia from January 1, 2023
This was announced by the acting head of the LPR Leonid Pasechnik.
The People's Militia of the LPR may become part of the Russian Armed
Forces from January 1, 2023.
"Today we are together, we are part of the Russian Federation. I
understand that from January 1, the People's Militia units will become
part of the Armed Forces of the Russian Federation," said Pasechnik.
On September 30, Putin signed agreements according to which the DPR,
LPR, Zaporozhye and Kherson regions will become part of Russia. The
project of the territories becoming part of the Russian Federation
implied that in all four subjects the transition period would last
until January 1. After January 1, all structures, such as the People's
Militia of the LPR, will become part of the structures of the Russian
Federation.