Following the official docs, the section on feature flags, I found out that my Identity component did not have the USER_RESTRICTIONS_ENABLED environment variable. I was able to add and set it true. After a while, I tested the process and it worked!
Now, if a user is not the assignee of a task, even if manages to start the process, they cannot see the task in their tasklist and get this notice:
Which clearly states the lack of permissions to see the task. If you confirm the workaround I will close the thread.