The process of aging, as it turns out, is malleable. It's most probably controlled by some signaling molecules in the bloodstream, it's just that we don't know yet which ones. Look up "heterochronic parabiosis" for related research.
Then there are Yamanaka factors, those not only erase cell identity, they also erase the age. Of course you don't want all your cells turning into stem cells, but the fact that this mechanism exists at all means that it's likely possible to isolate the pathway that resets the age of a cell but keeps the identity.
Then there's the "rejuvenation event" during embryonic development shortly after conception, as shown by DNA methylation clocks.
So currently we have these puzzle pieces that we don't yet know how to put together, and some are still missing. We'll get there eventually.
It's not even going to be life extension, as in, "you'll still get old and eventually die of old age but slower", it's full-on rejuvenation, as in, "you'll look and feel 25 and the only thing giving away your actual age will be your ID".
yeah, but you don't have to spend centuries toiling away as a slave for the Immortal Dictator
But most people would probably take the "you have to work an extra 100 years, but you get to live an extra 125" bargain.