You mean that some companies retain a cart for more than 30 minutes?
With Mouser, you can not only save your carts and/or projects. You can also give parts your own internal identification numbers/names/pcb designator. You can email your carts and/or projects to yourself or other people in case you don't trust them to keep your info. You can give permission for other parties to view your projects, only; or you can give them permission to edit the contents.
And yeah, your default cart is saved, even if you don't explicitly save it. Well as long as you are logged in while editing it. I've never lost a cart, anyway.
Whenever I am ordering components unique to a specific project, I will save the carts and put them into a project if multiple carts. When the parts arrive, I can put them all together with the name and date of the project/cart. So I can ditch the bulky packaging, for instance, and just give a small handwritten label to each component. "22uF 1206," and the fact it is part of the "[xxxx] project" means I can look up the project/cart name on my Mouser account to find the actual manufacturer part number and datasheet.
Mouser has an amazing website. They don't sell everything, but most of my admittedly simple projects are covered by Mouser. Usually I make my BOM just copying and pasting into Excel from my Mouser project/cart. Units per, designator, part number, description, can all be put in a Mouser project. Everything you need for a BOM; it might be a pain to copy/paste, but you also get links to the full datasheet, lead-time/stock, and current price. And a search bar to check for the latest and greatest (and cheapest). This is why Mouser is my first option.