While Steam will happily run offline, some things may happen:

- the game may refuse to start without internet
- Steam may after a while decide to reauthenticate and will refuse to run stuff

With no internet, you won’t be able to download any cracks, so either you should start downloading them now just in case, or get to brushing up your programming skills so you can write your own. I recommend the latter.

From a purely technical standpoint, you'll see what happens if you don't keep your PC or steam deck connected to the internet all the time.

Regarding steam, I've personally never had a problem with its offline mode, and I used it a lot many years ago. I don't think it's changed that much. There are even some games in steam that work even if you don't open them with steam, but they're mostly old games, like Two Worlds.
However, if you just installed steam and didn't open it (and it could also happen in some other way, though it hasn't happened to me) you'll be forced to login online. With no chance of the offline mode working if you don't.

There's also the obvious problem that if you don't have a game installed and don't have internet, it's not like when they were physical and could use the CD. And some games are taking up 100s of GBs nowadays, making it WAY more expensive to keep your collection downloaded the more games you have, if you ever wanted to.

Regarding each game's DRM, things are far worse:

-The EA app's offline mode doesn't work if you don't open it in online mode first, on each run.

-If a game is on an store other than steam, like Epic or Ubisoft, I don't know if they'll even let you play a game if it detected an update but you didn't update it.

-On the note of other stores, especially on Linux with different wine prefixes, Ubisoft Connect for example may forget your credentials and require you to login again (with internet).

-If a game is online only, then no dice. True even for games like Ghost Recon Breakpoint, which can be played entirely like a single-player game, and only requires an internet connection on the opening screen.

-If a game has Denuvo, if it's the first time you open it in a PC or some time has passed since you last opened it with an internet connection, you're out of luck. (And damarrin's suggestion is extremely hard with denuvo)

All in all:

-Emulators, gog offline installers, and indie or older games would be your best bet. Also physical CDs, if you have them.
-The latest AAA titles and other launchers would be problematic.

Many games on Steam are already DRM-free and can launch without Steam present. Steamworks DRM is optional, and these days many devs aren't actually bothering with it. Depends on what you play of course, but I'm almost completely disconnected from the AAA space so I expect most of my library's indies should be fine.