There's a manual in the mod folder. It's for older version, though.
You can also see the unit list on information window (the question mark on the left side on top of the galaxy map), like in vanilla. Just choose the required tab.

As Remnant you tech up by killing (not recommended) you current leader, or completing the project to advance the next leader. If you choose not to complete the project, next leader will automaticlly take control after 60 weeks pass.
The conditions of advancement and leader sequence are displayed in the before-mentioned tech tree tab.

Teching by CSA and every other faction requires killing the current imperial leader or waiting the same 60 weeks.

"How do factions like the Remnant and CSA tech up?"

I don't know about the Corporate Sector Authority, but some factions have a set roster that remains static throughout a galactic conquest campaign (e.g. all 'warlords', if I'm not mistaken - although the 'Pentastar Alliance' has a scripted event that gives access to a few, named units past week 20, there are also scripts around the conquest of a few neutral worlds that reward named, individual units which should be mentioned in the faction section of the somewhat dated PDF manual in the steam workshop folder).

Yeah it doesn't show them as a faction in the manual.
I was kinda hoping they would advance and we could use battledroids and droid craft as our primary weapons and they looked like they were the faction to have it
(B1s, Droidicas, Tank Droids, Lucerian Hulks) but without any advancement and having taken a level 5 shipyard to discord I got NO new ship access; just disappointing.

Maybe they will decide to mod in a battledroid focused faction or just make the CSA playable beyond a minor power.

CSA is not meant to be a droid faction, they are a corporate-based faction that uses old tech sold-off from previous wars.

Its only the main three factions that progress in eras and get different rosters, due to engine limits.

So is there a list of what they get? and when?

like what are the story triggers?

CSA does not progress, they only get MTC in era 4, but thats about it, they dont have any events or anything like that.

They need documentation for this mod on the front page.

Originally posted by Riekopo:

They need documentation for this mod on the front page.

If You have subscribed to the mod then the PDF manual (ICWv22Manual.pdf) is in it's steam workshop folder:

e.g. hardrive:\Program Files (x86)\Steam\steamapps\workshop\content\32470\1125571106

On it's website there is also a WIKI, containing similar information:

https://thrawnsrevenge.fandom.com/wiki/Thrawn%27s_Revenge_Wiki

However, the manual lags behind the state of the mod for at least one major update (2.2. to 2.3.).
Some more information can be gained by viewing videos on the modder's YOUTUBE channel:

https://www.youtube.com/channel/UC24e_8ncnLg-vptxVDNP-DA