But Raxxla may not be
in any of those colonised systems, it could be in any system visited during the human expansion to those colonies, or nearby but beyond that bubble. I think the 2296 date is intended to set a limit on the search radius, the radius being defined by those colonies. IIRC it was just before Achenar was colonised, which means Achenar had been discovered & explored by then, which sets the search radius at around 95 ly (going from memory, with only half a mug of breakfast coffee imbibed so far, so the little grey cells are only half awake!).
This to me is the likeliest intention of that first rumour date. So it (or perhaps the start of the “storyline” to find it) could be anywhere within ~100ly of Sol. The huge proviso to that hypothesis is that people had started long distance exploration trips of the galaxy even at gamma release (when I think the galaxy was opened up to everyone, before that it was limited to a small alpha/beta galactic test bubble). Now ED started in 3300, long after the 2296 first rumour date, so I dont think that test bubble is relevant BUT Raxxla could also be anywhere that had been visited and the pilot had successfully returned to sell the data to UC ( assuming FD have been strictly logical about its placement). The search radius could be increased if you took the furthest system position from Sol that existed in the original game (using ED distances), since that was really where the legend of Raxxla started...
So, the only thing we know for sure is that its probably alien (DW statement that it was covered in the alien lore book which has not been released or leaked to us), hence likely either Guardian or Thargoid. Given the preponderance of the triangular motif in the UC screen and very brief (IMHO deliberate obscuration, perhaps a
little bit obvious!) appearance in the ship’s nav panel, and similarity between that triangular motif and Guardian symbology, I am firmly convinced Raxxla is Guardian technology. Ram Tah’s decodes showed that Guardians were a space faring race that bioengineered races they encountered (often for hunting and eating!). Given the triangular motif in PF-controlled ship systems there is still a strong possibility lorewise that human evolution was engineered by the Guardians (wether as food, or as anti-Thargoid measure, or perhaps as successors; note to self, must watch Children of Dune on Netflix!) leading to the hypotheses that Raxxla is either in Sol or in Shinrarta Dezhra (PF HQ). This is all very tentative reasoning based on little supporting evidence. We also have Ram Tah’s statement that they had ark ships, so Raxxla could be one of those, now degraded by cosmic dust fall to resemble a moon, or engineered by the human cabal who control it into a human artefact such as a space station or installation (the latter have tunnels, for no sensible reason, which might be the omphalos).
Personally, following my “hunt the princess” storyline hypothesis, I’m still stuck on Aurora Astrum, desultorily searching in the dark (very long rotation period) for something that looks like an omphalos, losing interest and beginning to investigate an alternative (& ludicrously buggy) universe in SC.
Edit: TDW originated from the very earliest days of space exploration, which implies based in Sol. And yes, I’m also suspicious of Jacque’s journeying. I think most Orbis have engines- they’re the big things at the back!

but his journeying was suspiciously highlighted in Galnet, and his long life means he probably has some knowledge not available to us. He could indeed be part of/the originator behind TDW. This is another reason I decided to follow my “hunt the princess” hypothesis- Aurora Astrum is only 27 ly or so from him. Barkeeps hear many secrets, he could have heard of a strange discovery then guided the Rxxla rumour. IIRC the station he inhabits started out in a system near Achenar.