Looking at connect() function, there are several things which are raising questions.

project arg:
project is set as an optional arg:

But few lines lower it is checked for existence (thus, it's required, not optional): It seems to be pointless, as this arg is only passed to Spanner client, and the original Spanner client can handle an omitted project: it'll use google.auth.default() function to designate the project id from the environment. With this, I'd propose to drop this check and use project arg in the way of the original Spanner client.

instance and database args:
They are optional by definition, but in fact both are required. Probably, they should become required in definition (the function signature will be connect(instance, database, project=None, credentials_uri=None, user_agent=None):), so these checks could be dropped:

credentials_uri arg:
This arg looks divergent from how the original Spanner client is dealing with credentials:
https://github.com/googleapis/python-spanner/blob/b6b0348f5870f55c88b3cae44e229325fd755b26/google/cloud/spanner_v1/client.py#L123-L129

I'd propose to change this arg to use google.auth.credentials.Credentials class as it's done in the original Spanner client.