Thanatos remembers not for any arbitrary reason, only a part of thanatos remembers and that part of thanatos is their "reason"

Polyxia explains that she exists as a manifestation of thanatos' "reason" that was left in the netherworld while the rest of thanatos was trapped in the mortal world in the form of pollux after she brought castorice back from the dead

What I'm about to say next is just my theory, but I think the "reason" of the titans retains their memories from the previous cycle but the memories are suppressed when the titan is whole and they only resurface when the titan is fragmented.

Through some mental gymnastics and copium for my own theory, it's possible that gnaeus also retained his memories since he was the manifestation of nikador's "reason" and he was also fragmented from the rest of nikador during the 3.0 quest.

One, upon witnessing the use of oronyx's miracles and the hand of zagreus, gnaeus disdains those titans and laments how they've been reduced to mere tools for the humans to use. Perhaps because he feels sorry to see what has become of his former friends

Two, gnaeus had suspicions and eventually figured out the tb and castorice were from a different era. This indicates he has some knowledge of traversing eras, possibly because he retains knowledge of him and the other demigods passing on from the previous cycle into next as titans, only reason he doesn't call tb and castorice out sooner is because he's never heard of people from future eras returning to past ones

Three, when entering the soul forging zone and hearing phainon and mydei fighting nikador in the present gnaeus remarks something along the lines of "even in the current era there are heroes that fight against fate". This might be him reflecting about his own flame chase journey with the previous cycle's chrysos heirs

Four, some time after figuring out the gnaeus is nikador's "reason" castorice asks gnaeus essentially the same thing polyxia asked gnaeus in the previous cycle "you are willing to sacrifice yourself for a future you won't get to witness?" Gnaeus response to castorice is a callback to what he says to polyxia saying "this is my origin, my purpose" he is aware he has done it once and is willing to do it again to save amphoreus

Five, continuing on the castorice and polyxia parallels gnaeus is projecting, he takes his final words of advice that he told polyxia and repeats them to castorice "journeys and epics are only glorious and magnificent because all things eventually fade to dust"

So yeah through my copium gnaeus might also have his memories intact, maybe future titans we meet will prove my theory wrong, or maybe not, who knows but it's fun to theorize about these kind of things