Most people who rely on it are business, and they stay in to compete with businesses who are also in it. If nobody has access to it they will just rely on other means, their own personnal website, other social medias that would fill the gap...
Most individual would be annoyed at first as well, but then all end up migrating to the another thing once the dust settle. More than facebook, this would be more the loss of instagram and whatsapp that would annoy them but they would easily move to telegram and signal. Many non-tech people already have a telegram account for example but don't move out of whatsapp because they are all on it already. Nobody wants to be that guys asking anyone else to abandon the group and move to somewhere else just for the heck of moving. As for instagram, they would quickly switch to tiktok, snapchat or something else that fills the gap.
I'd like to think open source and decentralized tool would have en edge but I am very doubtful it would happen. It is always easier to migrate to a single jail cell than being free.
Anyway, Facebook/Meta has just filled a form to cover their ass. They aren't threatening to leave EU. If they have to keep and manage the data in EU they will find a way. It will just be costly and hurt their finances hence the obligation for them to mention the riskier route.