Maintain cart for a week in Magento 2?

You can set it from admin configuration.

Admin >> Store >> Configuration >> Customers >> Persistent Shopping Cart >> General Options >> Enable Persistence.

set it as Yes.

To update Quote Lifetime, Go to:

Admin > Store > Configuration > Sales > Checkout > Shopping Cart > Quote Lifetime

To Enable Persistent Cart (A persistent shopping cart keeps track of unpurchased items left in the cart, and saves the information for the customer’s next visit.), Go to:

Admin > Store > Configuration > Customers > Persistent Shopping Cart > General Options > Enable Persistence

Set Yes

This 2 setting Enable us to manage cart better and reduce cart abandonment rate.