You... serious about immortality. AKA not serious.
What is your model? Quantify it.
Here, I'll do some basic scenario / math for you. Assume immortality and death rate converge with that of accidents fatality per 100k, population will increase by 0.75% per year at TFR 1.1, aka by 2100, PRC would have ~2 Billion people with 1.1 TFR with minimal death rate (cause if you've got immortality, you've also cured all of the diseases). That's how fucking stupid / not viable your idea is based on 2nd/3rd order consequences. And net pop would only grow, because then natural desire for having kids even with SHIT TFR would rapidly outgrow aggregate deathrate. Then you have opposite problem, but at much worse magnitude, people stay in jobs forever, no prospect for upward mobility because social structure will be entrenched. Even modest increase to 150 year life span = 1.4B population by 2100, 2B by 2150 w 1.1 TFR. @1.5 TFR, that's 2B by 2100, 2.4B by 2150. Then what? Pregnancy licenses for population control? You going to pick a system to choose who to hunger game / purge system based on dwindling resources, or is part 2 of plan aka "draw rest of owl" to get fusion / abundance / dyson sphere? Is that totality of your solution? Speculative AGI magic hopium?
PRC / CCP has done family planning before. It's one political system that has done massive demographic engineering. Historically societies have had much more kids under much worse conditions (i.e. post famine, post war). Indoctorinating and building system around contributing births to state is not unfeasible under right incentive / indoctorination structure.
Mass opposition can be managed. Emmigration can be managed.
The problem with thinking if AGI will work or not is the OR NOT. Need to manage alternatives in case of NOT.
Regardless, LBH, fundmental to these proposals is the notion that PRC wants to stay dominant Han. It could just do massive, massive immigration + sinicization and deal with hot mixies.
If AGI/amortality-tier tech exists, then so would automated energy and resource production tech, meaning the Earth can easily support 50-100 billion humans. More with solar system colonization and space habitats.
The CPC is not omnipotent. At least 50+% of the population (at a minimum, women + fathers of daughters) will not accept bureaucrats attempting to Chinese society back to fedualism. Remember, part of the raison d'etre of the CPC was women's equality. Mass opposition to extremist proposals of this magnitude cannot be managed.