I may have got it wrong regarding the Intaki Assembly bit, and this might exist for Jin-Mei and Mannar too. As in, there may be 62 districts and 3 assemblies (similar to Russia having multiple types of subdivisions).
In RP, fiction and whatnot, there's always talk of "Federal" institutes...what about exploring district things? District courts, district parliaments, district laws, district politics...I think however, that the use of Federal foremost is that they are the most likely ones to have the most influence/authority over capsuleers (a capsuleer that strolls out of their areas of station, or walks around on planet, is going to be subject to local law IMO). Even lower than district, apparently the systems vary.
Moreover, perhaps party lines are being downplayed to distance it from IRL? Abraxas was extremely creative in regards to the Gallenteans in TBL, perhaps he wants to plan something similar in regards to outlining Federal government and politics? Maybe a more SW Old Republic thing, of having planets with a wide variety of different systems (all adhering to basic constitutional tenets), and their own governance, but with a Senator. No parties as the Federation may be too diverse to be able to consolidate political opinion.
One of these things. We'll See™ once this immersion project is finally updated. I think one of the biggest assumptions people make is that the Federation has monolithic control. The Federation is a federation.