Is "Deferred Payment" a custom payment method you added? I don't see it anywhere. I am able to create a payment method, and it does show up as a choice in the Payment Method field in the Manage > Payments > Search Payments section.

Hmm, maybe I deleted it because I wasn't going to use it. I don't see it in Configure > Payments > Methods. I'm not live with v 9 yet and haven't worked on it in a while.

Oh, I see what you mean. I didn't realize that was an option when entering an order via Admin. I'll try to test it tomorrow to see if I see the same thing you are.

I tested with a deferred payment, and I do see the same thing; since there is no payment record, there is nothing to be returned in a search of payment records, so it doesn't show up on the Manage > Payments page.
I can see where it would be handy to have them show up somehow on that page, especially if someone is using that screen as a list of "here's the orders I need to follow up on for payment". One possibility (so the existing search code wouldn't have to be changed) would be a separate section or button to "Show Orders with Deferred Payment" (or even a more generic "Show Orders Without Payment", in case something odd happens and there are other reasons why an order doesn't have a payment).

Another idea (which would still be show up on the Orders page not the Payments page) would be to make "Deferred Payment" an order status that is set when Deferred Payment is chosen, so someone could search on that. Or, in your specific use case, have a "Quote" order status that you manually set (or automatically set with a customization) when you enter an order with Deferred Payment, and you could specify that order status on the Orders search page.

Or, create a "Quote" payment method using the "Purchase Order" Instrument Type, and use that instead of selecting the Deferred Payment option when creating the order. Then there would be a payment record, and you could filter on that payment method on the Manage > Payments screen.