I would create new databases, but it depends. In principle, what your boat is floating :)
one database for each user:
+ security is easier
+ asynchronous concurrent requests (if your server can handle this)
- a bit heavier on disk
one database:
+ one file for processing instead of a bunch (if it is +)
+ a little more free space
- slow when data reaches large amounts
- simultaneous connections do not mean that a heavy sql request from one user will use all the others
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