How is the Product Backlog ordered?

>This responsibility is solely carried out by the product owner.

The Product Owner has the final authority over and accountability for most content and ordering (not prioritizing) of Product Backlog Items. With respect to ordering Product Backlog items, the Product Owner may enlist input, support, involvement and work from others. From the Scrum Guide: "The Product Owner may do the above work or may delegate the responsibility to others. Regardless, the Product Owner remains accountable."

The breaking down (sizing) of Product Backlog Items is done by the Developers who will do the work. From the Scrum Guide: "The Developers who will be doing the work are responsible for the sizing. The Product Owner may influence the Developers by helping them understand and select trade-offs."

The delivery order (ordering of Product Backlog Items) is arranged so as to maximize realized value. From the Scrum Guide: "The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team."

Because items at the top of the Product Backlog are closest to delivery, they usually benefit from the most attention and work in Scrum planning activities. As such, Product Backlog Items near the top tend to be the most broken down (smallest) and best understood items on the backlog.

See: https://scrumguides.org/scrum-guide.html

By whatever is deemed most appropriate by the product owner.

The product owner is the person responsible for prioritizing the backlog. Product order is done by whatever is deemed fit by the product owner.

The product backlog is not ordered by small items at the top to the large item at the bottom, it is not ordered by safer items at the top to riskier items on the bottom, by least valuable items at the top to the most valuable at the bottom neither is it by items that are randomly arranged. This responsibility is solely carried out by the product owner.