Worked at a large B2B SaaS from near beginning. You want a hybrid; shared DB, but with the ability to move to a 'shard/pod' architecture where you separate out your customers/users into different dbs / apps servers as you scale.
We did it about 3 years in, when DB became a scale challenge. Eventually you'll also get to the point where you want to be able to rebalance and migrate data between each shard.
All of this is nothing you should be trying to solve too early; i struggle to think of any real benefits of single DB per user, unless you are separating out all architecture- including app servers - and that might only be relevant for large enterprise customers? Selling in that market is hard.
We did it about 3 years in, when DB became a scale challenge. Eventually you'll also get to the point where you want to be able to rebalance and migrate data between each shard.
All of this is nothing you should be trying to solve too early; i struggle to think of any real benefits of single DB per user, unless you are separating out all architecture- including app servers - and that might only be relevant for large enterprise customers? Selling in that market is hard.