What? I've been to the Slaver's Guild multiple times and never saw an "Offer your servants" button. Is it hidden in a weird location? Do I need to have more than just starting servant? Quest locked in Story Mode?
"Offer your servants" is offered unconditionally at all slave guilds, usually as the second button (it can move down if options for side quests are listed above). It is unaffected by game mode or slave count; you can sell the starting slave, though that's generally not a good idea.
Do you have any mods installed? That is the only thing I can think of which would cause that to change as it has been that way for several years.
The game is quite stable, but now and again we see unique problems with specific computers. In the appdata is a folder for logs (on Windows, %appdata%/Strive/logs)(Edit: if you installed through the itch.io app, it may be in a weird location and be easiest to open it in-game through the mod menu's "Open Mod Folder"). The godot file should list any errors that occurred (edit: updated when program closes), though the last 8 lines will be normal errors related to closing the game. However, as of version 1.0d the game no longer runs in debug mode and most errors end up crashing the game instantly, so I have doubts that it will show anything useful. Especially since it is very unlikely that only that button would missing, rather if there was a problem the slave guild would either not show up or behave as a softlock.
Well there shouldn't be anything there now since I've uninstalled it, twice now. Never had any mods.
(Edit: Apparently there is still a log there despite having uninstalled it, but the log only has Godot warnings, no game errors.)
Quite frankly though, if a game has mods, chances are there's something un-fun or problematic about the base game.
Well it seems that the actual problem is on your end. Just in case, you can compare your game to these screenshots. They were taken at the places, where you seem to have a problems: slave menu and stat list, slavery guild and all the buttons. Also, I completely disagree about your statement about mods. There is no perfect game, but mods can help you to customize your experience, making gameplay exactly as you want it to be. For example "Gigastructural Engineering" mod for Stellaris adds tons of fun staff to play around with, but it is quite unbalanced and would be a bad idea to include in a vanilla. There are also tons of mods for different games that tend to overhaul them completely, so you could enjoy your old games with a new spark of interest. Anyway, here are your screenshots, hope you will be able to identify your problems and fix them:
