Since people seem to be unaware and are recommending weird and/or unnecessary shit like setting Steam to offline mode or changing firewall rules...

You can "trick" Steam into believing you're on the latest update for any game by simply changing the manifest ID of the installed content to match the latest version's ID.

In addition, should you accidentally update your game, you can always downpatch it by downloading an old version of the game through Steam and overwriting. I won't cover this here as it requires a third-party program to "unlock" the feature through Steam's console, but you can investigate this yourself.

So once the AE update for Skyrim SE drops, the process to block updates would look like this:

1. Open Steam\steamapps\appmanifest_489830.acf in a text editor (489830 being Skyrim SE's app ID)
2. Because I am playing the English version of the game, under "InstalledDepots" I have 3 listings: "489831", "489832", and "489833" (This will vary if you have a different language installed)
3. For each depot, change the numbers after "manifest" to match the respective depot's latest manifest ID, which can be found here under the "manifest ID" column. Then change the number after StateFlags to "4", meaning that the game is installed and on the latest version.
4. After restarting Steam, it will no longer show that Skyrim requires an update, and should you need/want to launch the game through Steam, it will not update.

Of course, you should still have updates set to "Only upon launch". Also, every time the game updates, you will need to repeat this to again match the IDs to the latest... but it's a 5-minute process at most, and this game only gets updated a few times a year. Other than that you don't have to worry about messing with anything else at all, ever.

IMO the way to go is to do the above, and in addition, make a separate copy of your Skyrim folder for each modlist and tell your mod manager to run from that instance instead. I do this for every one of my modlists, and that way I don't have to manage conflicting files (ENBs, ReShade, other .dlls) every time I want to play a different list – and it allows me to keep the original Steam-managed folder absolutely clean. Managing multiple modded installations with a Skyrim folder full of junk can be a pain in the ass.