Lots of makers buy raspberry pis with screens. You can buy those online, or maybe even from a store like Microcenter with cash or gift card. Some stores might take sats.

Pretty sure the government doesn't know what I 3d print on my printer...

It being unique to you doesn't mean it harms anonymity unless you are posting it publicly under your name... I guess the other option is to post it publicly under a psudeonym so other people can build it for themselves.

I think the hardest thing about this device would be input controls for browsing the web... That would be tough. Touch screen might help.

I doubt you are going to find a device like the one you are searching for in a big box store because its precisely the thing that would take a lot of support, would probably advertise to you, and would probably have trackers and analytics like crazy to capture location, browsing history, etc. The incentives aren't there for a company to build a privacy-minded device like this.