I'll give you a hand with the chronological ordering on these
TN was put into Carcosa in a 'special' BGS way with super-influence and virtually gteed expansion which ran into another BGS power. (I used to think something else but now think its purely MB was a fan of Lovecraft and took the opportunity with Carcosa, I dont now think there is any more tinfoil, he was just giving them a good start and a chance so they didnt get wiped out immediately is all)
TN was adopted by 1 o r more player groups / squadrons over time but either gave up or got nowhere
Carcosa was taken by a pmf EN and held while TN were unsupported and just an NPC group?
This is where it gets murky. Especially as to chronological order.
DG2 was an SDC event. Everybody who knows about them will have their own views on SDC or on one member who killed Salome. Start another thread about that.
TN was adopted by LR and LR moved to Colonia and took control of Carcosa from EN who were a pmf. Seemingly with no negotiation? We have the date from Isiah, the accusation is it was taken while the pmf was out exploring and maybe even as revenge, when did DW2 end? One side says liberation one says retribution.
At some point LR declared war on Colonia Council and a new 'council' was the eventual outcome. Point of a sword negotiations?
TN have not remained in Carcosa but have been accused of expansionist behaviour which they deny. They have now been retreated back to Carcosa.
March 3303 ish: a new 'council' was the eventual outcome
(if you're referring to the CEI groups rejecting the claims to authority of the original CCN)
June 3303: TN was put into Carcosa in a 'special' BGS way with super-influence and virtually gteed expansion which ran into another BGS power. (I used to think something else but now think its purely MB was a fan of Lovecraft and took the opportunity with Carcosa, I dont now think there is any more tinfoil, he was just giving them a good start and a chance so they didnt get wiped out immediately is all)
October 3303: At some point LR declared war on Colonia Council
(They lost, massively. This was an official Frontier CG)
August 3303 - January 3304: Carcosa was taken by a pmf EN and held while TN were unsupported and just an NPC group?
(EN captured Robardin in August, would have captured Aragon in October if it hadn't been for the CG interfering, eventually got chance in January)
Various times in 3304, and February 3305: TN was adopted by 1 o r more player groups / squadrons over time but either gave up or got nowhere
January-May 3305: DG2 was an SDC event. Everybody who knows about them will have their own views on SDC or on one member who killed Salome. Start another thread about that.
March/April 3305: TN was adopted by LR and LR moved to Colonia and took control of Carcosa from EN who were a pmf.
June/August 3305: TN have not remained in Carcosa but have been accused of expansionist behaviour which they deny. They have now been retreated back to Carcosa.
(they still have presence in the Earth Expeditionary Fleet system for now, and will be difficult to remove from there in the short-term)
June 3305: when did DW2 end?
August 3305: Point of a sword negotiations?
(EN-LRCV treaty signed following a failed attempt in July 3305 to retake Carcosa for EN)
(to highlight the two things most likely to be considered "expansionist behaviour" and to put them in the timeline: in terms of Colonia politics it is not
usually considered expansionist merely to be present in another system, because the political geography makes that the default arrangement)
September 3305: have been accused of expansionist behaviour which they deny
(No Look Here Gang capture Pennsylvania with Nameless support)
December 3305: have been accused of expansionist behaviour which they deny
(Nameless capture Earth Expeditionary Fleet system)
... and then relative to the current conflict
February 3306: Societas Eruditorum assist the Colonia Council to retake Pennsylvania from the No Look Here Gang, current conflict begins.
I would add something else to this as the whole player named/FDev named factions issue muddies the waters where perhaps it shouldn't.
Possibly, though I think the actual issue is slightly more fundamental and doesn't hinge on who named the faction.
Essentially, that by two years in factions with supporters had already claimed all systems - with relatively little direct fighting over who got what - so anyone trying to take an additional system for any faction therefore has to fight against an existing supported territorial claim. That applies to the Nameless taking Carcosa from EN ... it would also apply to a hypothetical [1] Radio Sidewinder attempt to take Ra' Takakhan from UCA.
In Witch Head, for example, all the factions are Frontier-named. A single group has nevertheless supported its adopted factions to take control of the entire nebula there, and anyone who wants a system under different control will have to fight against that existing claim, with greater strength than the holding group can defend with.
The Nameless are unique for Colonia in that they actually had the strength to take the system, against an actual attempt to enforce the earlier claim. (And then a second system for EEF, and then support the NLHG to a third - though those were less directly defended)
[1] Picking a geographically implausible example deliberately, here.