Spring Session/OAuth2 multi tenant application / multiple cookies - spring

Question

I used Spring Session and OAuth2 to build a SSO for a multi tenant application and have an Application with different frontend clients and a backend server.
(I used this tutorial https://www.baeldung.com/sso-spring-security-oauth2).
So the problem now is that each client (Tenant) runs on a different domain than the backend server and so the backend server has only one cookie and a user can't login with on two different tenants at the same time. (Each tenant has different bearer tokens so only the cookie is the problem)
The Idea would have been to somehow configure spring to create a different SESSION cookie on the server too (Which I didn't manage to do/Don't know if this is even possible)
And additionally I don't understand why I need that cookie, since I am using a token based authentification.
I do understand that if I want to automatically log the user in if he closes the browser and opens it again, that I need to save some data on the client side (e.g. a cookie, but why use a JSESSIONID for that and don't save the bearer token in a cookie)
Additionally I do belive that after the login process the session cookie is used for authorization and not the oAuth token. (I removed it from the token store + refresh token and on the next request it simply created a new one)
So basically what I want to know is:
Can I somehow configure my backend to create one cookie per tenant ? (without running multiple instances of it)
Why do I need the session cookie ?
How is the user reauthentificated in oAuth after I delte the tokens from the token store, without having to enter the password again (I guess the session cookie is responsible for that tho)
My yaml config looks like this:
server:
port: 8082
servlet:
context-path: /ui
session:
cookie:
name: UISESSION
security:
basic:
enabled: false
oauth2:
client:
clientId: SampleClientId
clientSecret: secret
accessTokenUri: http://localhost:8081/auth/oauth/token
userAuthorizationUri: http://localhost:8081/auth/oauth/authorize
resource:
userInfoUri: http://localhost:8081/auth/user/me
client2:
clientId: SampleClientId
clientSecret: secret
accessTokenUri: http://localhost:8081/auth/oauth/token
userAuthorizationUri: http://localhost:8081/auth/oauth/authorize
resource:
userInfoUri: http://localhost:8081/auth/user/me

Answer 1

How OAuth2 works would be as follow:
The access token is granted for that tenant only and can't be used to access resource of other tenant.
The tenant website then need to store this access token to use later, either it can be stored in:
Cookie - you have no issue as each tenant have different domain.
Local Storage - you have no issue because it's also different storage.
SESSIONID is the cookie created by Spring and will not be used in this case.