I mean, it could be both where reincarnation is only possible within a certain bloodline, but that's just me throwing crackpots.
Just to be clear, I subscribe to the reincarnation theory more, if only because I theorize that Orion's soul is older than he is and could be the reason why Luna couldn't get a read on him (hell, I wouldn't be surprised if the 'eternal soul' that Anima is a warden of - which is one of her many titles thrown by Caly when mentioning her - happens to be Orion's). It's also because I don't subscribe to the 'time loop' theories, and believe instead that the current state of Eternum* is causing certain patterns to emerge instead of events outright repeating themselves as is (which is one of the theories floated on the official Discord, that Orion saving Caly from imprisonment is a "pattern" that is similar to the Eldari freeing Anima...though not exactly sharing the same variables and/or circumstances).
That said, I don't think Orion is some sort of Founder (or a reincarnation of him), though it's possible that he could end up becoming one in a potential Bad End (I still think becoming CEO of Ulysses is going to be a bad end of sorts). If anything, it's possible that the Founder is instead Y'liar - that is, Anima's former captor from Caly's tale - and that the reason he's noticed Orion is that he might have detected a sense of familiarity on our horndog of a protagonist (which makes more sense if Orion happens to be the reincarnation of the Eldari...or someone housing his soul ala Astaroth from OIAL. But again, that's just one of my crackpot theories).
*(The detailed version of said crackpot theory is
here (disregard what I theorized about the Founder's identity and true goals are in that theory, since that was made prior to 0.6). But in case you don't have time for that then the TL;DR of the theory is that
prior to the events of the VN, the Founder altered the linear progression of life and death throughout Eternum/the Astral Plane by closing the gate to the afterlife (Acheron) and trapping the souls of the dead in a cycle of death and rebirth. This is possibly to manifest the Gems of Doom, as the Red Herring event and the Ion announcement (where a GoD is found in the Styx server - a name associated with the Greek River of the Underworld) seems to imply that said gems are associated with death and/or the dead. This, of course, causes a laundry list of problems to emerge ranging from the dead being pissed because they can't pass on to the actual inhabitants of Eternum (i.e. otherworldly creatures) being pissed at this sudden influx of "players"/astral bodies invading their personal space and are starting to push back (hence reports of increasing monster activity on servers). Regardless, Orion is supposed to fix this mess, hence the dead and Idriel/the Lady in Black asking him to "break the chains")