Can cat fleas survive off my pet birds and are my efforts not enough?

Hello, I’ve been looking through this site and can’t find an answer to this.
We do not have a dog or a cat but unfortunately some stray cat had kittens under our house without our knowing where we couldn’t remove them, the mother moved them and now a week or two later the fleas have migrated indoors looking for food.
We only have laminate flooring in the house besides our 1 large rug and 2 floor matts which I have sprayed with flea spray and vacuumed thoroughly twice now (and will do every day until thursday). Our little vacuum does not work well at all on the laminate flooring so I don’t usually vacuum it, do I need to vacuum it anyway?
I read fleas reproduce poorly off of humans and may disappear after awhile but didn’t find anything about birds. I have 3 small parrots and I’m worried the fleas could transmit a disease to them from outside or that they will be able to survive on them. I’ve seen no fleas on them and I’m hoping it won’t be an issue but I’m worried.
I’m also trying to avoid using any flea treatment directly in the house because of the birds, I dragged the rug, matts, and couch outside and sprayed them there to be safe. Birds are exceptionally sensitive to aerosols and toxins and I’m worried that any contact with any poison or residue from bug bombs could kill them even days after.
I don’t want to use flea treatments directly in the house except as a last resort since I’d have to relocate my fish, snakes and birds to a pet sitter for a week in order to safely use them.