I'd be over the moon if I could find a way to get this done for less than $10,000.
As a stopgap , has anyone made something like a Raspberry Pi zero, but even smaller( a single USB port would be nice too) ?
This project highlighted on Hackaday might give some inspiration too if you're willing to look beyond.
https://hackaday.com/2022/01/03/another-homebrew-linux-board...
$10,000 sounds like a nice tidy price if you're trying to get a small quantity of boards built and shipped.
You didn't mention how much you have designed so far. Is this just an idea, or are you all the way to a schematic with bill of materials? The closer you are to the latter the cheaper it gets. And if you DO have a gerber/BOM, there are turnkey services that can build the boards for you outright, like PCBWay.
As far as PCBs and stuff, I literally have no idea how that works. I would definitely need to pay someone to design it for me.
I do mostly firmware but lately I've been working with someone that builds his own hardware. Maybe we can get you all in touch.
Pico and rpi are completely different levels of effort and cost. You should figure out what networking, ram, OS or RTOS, and cpu power you need first.
I'm not sure if this is a great idea (for anything beyond a hobby project) as your customer will have to supply the Raspberry Pi Zero or Zero W.
You cannot purchase Zeros in quantity (there are limits imposed).
You will be better supported by Raspberry Pi if you go down the Compute Module path (yup, they're more expensive).