I believe the 3I "tolerates" the Federation of Arden, as you call it, but is not recognized by the 3I in a legal sense.
Before FFW, my take is that Arden was able to expand by profiting its position in the Demilitarized Zone amont the Zhodani Consulate and 3I. Neither of them could intervine without raising the other suspictions (at least)
Arden is a TL9 world claiming sovereignty over a few systems on the fringe of the Imperial Borders. It possesses no method to replace lost or destroyed starships (their Class B Starport is unable to build starships) except through import.
CT:HG, page 20:
alternatively, a planetary navy may construct ships on its planet, using local resources, even if a shipyard is not present.
So, Arden may construct or replace ships, though its low TL will limit their capacity (at least until they absorbed Tremous Dex, after FFW).
This region of space loses political significants as relations between the Imperium and Zhodani normalize post-FFW. In the meantime, the 3I supplies these necessary starship imports as a control mechanism for this "area of space."
The region keeps being a demilitarized zone, and its importance is not diminished (as has not in any inter-frontier wars period, despite how long it can be and how normalized elations among Consulate ans 3I are).
Again my take, is that Arden profited the after war period to expland, but also it was allowed to expland, mostly by the 3I, to neutralize both Quare and (more important) Tremous Dex as pirate bases.
Both are B class starports with low population. Specially Tremous Dex, with its (relative) high TL and low law level is quite likely to be one of the major piracy centers in the whole Marches. Few (if any) worlds are better to repair your ship or conduct maintenance, or to clear your "adquired" goods if you are in piracy trade, and its position in the Demilitarized Zone protects it against Imperial action if they don't want to enrage the Zhodani.
So, again as I see the history of the SM (so it can be considered, at least partially, as IMTU, albeit one very close to OTU), 3I not only allowed, but encouraged (and probably covertly helped) Arden Federation (then in good terms with 3I after having sized for them in FFW) to take both planets. Zenopit and Pequan mostly were absorbed to keep the comunication lines of the (mostly J1) Arden Navy.
In this scenario, the Zhodani did not opose it because its recent defeat (but see that Arden did not expand towards them).