With 3 you are splitting your application into multiple services. When you distribute your code across multiple services, you increase the level of indirection. The more indirection you have in your codebase, the harder it is for one person to work across the entire codebase because they have to keep more things in their head, and working across network boundaries requires a lot more code than working across files, and finally it's harder to debug across a network API.
Now, this doesn't mean that it's bad to split your application into multiple services. Doing so will help you scale your application as you can scale only the pieces that need scaling. Perhaps more importantly, splitting your application into multiple services makes it easier for more people to work on the codebase at the same time, since they have to adhere to the API contracts between the services, and are less likely to be working on the same files at the same time.
So 3 is a good choice if you have scaling issues, either for load on your application, or the number of developers that will work on it.
1 is a good choice if you want to move as quickly as possible and can put off scaling concerns for some time.
2 is the worst of both worlds. Your two services will be coupled by the database schema and will be sharing the same database instance. The separation of code means that you have extra indirection, the database schema coupling means that you won't fully get the people scaling benefits, and since most applications are bottlenecked by the database, the sharing of the db instance will deprive you of scaling independently for performance.
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