"The Product Owner proposes how the product could increase its value and utility in the current Sprint." Page 8 of Scrum Guide 11/2020.
The phrase you are quoting is from the comparison table and I had to break it down somehow and thus the PO is managing the tasks (of the backlog) and assigning them to the team is definitive true. BUT the whole scrum team then decides which of them are taken for the next sprint.
Can you otherwise explain who is responsible for making up tasks for the team?
Also, Development Team and Developers, these are just synonyms for the same thing. Don't mind that detail.
Furthermore, this article is about Scrumban, all details about Kanban and Scrum had to be compressed to not lose the point of it.