I'm going completely off of vague memory here bc i managed to find the hireling dialog not too long ago, so be careful here, but you can use a program called dnSpy to open the assembly file and look through its code. I do not remember where I found the hireling chatter specifically, but I'm sure with enough digging you'll find the Phobos pause lines. You could probably do a ctrl+f search and type in one of the pause screen texts, probably one of the ones relating to the discord since none of the hirelings ever mention #firing-range or #mess-hall in their chatters. I'll do some digging myself and see if I can't figure out where they're stored and give a little pathway down to them. Might also relocate the hireling chatters while I'm at it too.

Edit 1: use ctrl+shift+K to better search the whole assembly. crtl+F only searches the current file you have selected. Also use the assembly you have in your managed folder, not a fresh install. From my experience, using a fresh install causes all of the custom data to just. not be there. I know just about nothing about assembly files, so it could be some interaction with the game and its other files, perhaps the mod itself, but regardless. Use a used file.

I've found the Hireling chatter once again, but no luck on the pause text so far. If you, or anyone else wants to find the hireling chatter, here's some basic instructions:

1: Open dnSpy and in the top left, hit open and then navigate to the assembly file you currently have in your MPN managed folder. Or make a copy of it before hand and store that somewhere else and use that file.

2: Once opened, hit Crtl+Shift+K to search through the entire assembly. Ctrl+F will not work for this step. Type in "hireling" into the search bar that opens in the large window on the right.

3: Scroll through the search results until you find you find labels that say "string[] phrases_" there will be an additional word after the underscore that indicates what context the phrases will be used. phrases_Bye for example are the little chatters that trigger when you walk past a hireling's interact radius.

From there, you can edit as you please. Make sure EVERYTHING IS CONTAINED IN QUOTATION MARKS AND SEPARATED BY COMMAS. Otherwise, the dialog will not register and could possibly cause issues.
you can use %NAME to make a hireling refer to you by name. I know there are additional parameters, one of which I believe can get a hireling to mention another hireling by name, but I do not remember exactly what it was.

I am still searching for the pause text. I will post a new message when I find it rather than edit this now already massive message.

I'll skip a fair share of things since they are mentioned by FR3NZY

You can only edit the assembly that is within managed, because it needs to reference additional files, since if you do try to edit one outside of it, you will get a fair share of extra errors and even outright not allow you to save your changes.

The pause menu quotes are at UI_Menu -> AllFlavourText.

All the hireling quotes are at Squad_Hireling:
phrases_Bye - When the player who once was near a hireling gets away from them
phrases_Fired - Unsure what triggers it, might require you to fire a hireling present within the HQ, and get near them as they leave the building
phrases_Hello - When the player gets near the hireling will pop up one of the messages in it
phrases_Hired - Unsure what triggers it, might have a similar condition as _Fired
phrases_HireMe - Used by hirelings that are waiting near bossman to be recruited
phrases_Neglect - No clue
namelist_<type> - Listed names that hirelings can spawn with. The Field or namelist's are required to be listed in the DefineAllNames Method to actually make them appear in-game. Note that if you want the custom names to not have their letters randomized, go to GarbleName Method and edit the last value on the first line to a number such as 99, which makes it so that hirelings with names only with over 99 letters will have their letters on the names randomized. [end result = "while (inGarble > 0f && inName.Length > 99)"]

♥♥♥♥♥♥♥♥♥♥ i was scraping through UI_Menu and somehow never checked AllFlavourText :sob:
well there it is lol

and yeah I've no clue whats up with Hired and Fired
I don't think I've seen any unique dialog regarding those topics, but maybe I was just never within range of the hirelings when it happened.
Neglect also feels unused, absolutely zero clue what it would refer to. Looking in the vanilla Assembly, the only phrase in the neglect string is "I thought we had a thing, %NAME.". It looks like it should be a part of the Fired phrases, but it's its own thing apparently.