Oh it's okay, it's a single-player game, it's not that you need any server capacity for that. Other than download servers but it's Steam's problem, not publisher's.
They have a cross platform save sync service which has been disabled, but it sounds like that wasn't load related. I'm not sure how big the save games are but 700k people mashing the quick save button every 30 seconds probably adds up.
I have a total of about 75 saves: quick and auto saves are limited to a rolling 25 by default, plus about 25 manual saves. Steam shows I have used 795 MB of space, so they're not _big_ but they're not small.
They are a pain. I'm 9 hours in and at 1/17GB in Steam Cloud. I've been going between my Mac and an ROG Ally and syncing saves takes upward of 3-4 minutes and sometimes just fails silently (loudly if you launch the game, but still fails). Steam is definitely not built for that, considering that piece of the user interface barely gives any feedback.
It might be related to multiplayer or that one had to redownload the game. The EA was so different, you had to uninstall and then install when it unlocked globally. No preload available.