You said it was a single spartacus project, but let me try to share our own experience in case it gives you an idea. We did 2 different spartacus projects and 1 backend project.

When you use multiple sites, the baseSite value is added to the end of the user ids on the hybris side. This way, user sessions are not mixed.

For example;
[email protected]|site1
[email protected]|site2

For build/deploy operations, you will define each site in manifest.json: https://help.sap.com/docs/SAP_COMMERCE_CLOUD_PUBLIC_CLOUD/b2f400d4c0414461a4bb7e115dccd779/1c26045800fa4f85a9d49e5a614e5c22.html