Are there any cameras left on the market that don't require the video to go through some external cloud service (aka somebody else's computer)?
Yes. They are known as "IP Cameras". Mostly you find them marketed as security cameras which are intended to send their signal to a centralized local security camera hub. Basically, like in the old CCTV days, except, instead of a video cable, the camera connects with an ethernet cable, and instead of a CCTV security camera hub, it's a server doing the same job. That market still exists and is still full of products. The biggest player in that market seems to be
Axis cameras from what I can tell.
The line is blurred though. Many of these devices can do both: Working as a regular IP camera, while also simultaneously being able to send the video to a cloud service. But the original LAN-only market still exists, and the identifying keyword for the local-LAN side of it is "IP Camera".
One example of the blurred line is with those Axis cameras I mentioned. By default, most of them are just IP cameras, but can have additional streaming software added to them,
CamStreamer, which adds the ability to stream to a cloud service of some kind.
Another example is when you have a camera which, out of the box, works as both an IP camera and also as a camera which streams to the camera manufacturer's own cloud service. I'm using one of
these Reolink cheapies for the
CrowCam. It does both things out of the box. My Reolink camera streams via its ethernet cable to the security camera hub software that's built into my Synology NAS (called "Surveillance Station"). The video is a local LAN stream at that point, then the Surveillance Station software has an additional feature I can activate, which sends the camera's stream up to my YouTube channel. That keeps everything under my control.
That same camera also connects to ReoLink's web service. I don't actually know how to turn off that side of it. My guess is that they don't have a way to turn it off. However, it's useful for command+control of the camera itself via their smartphone app, so I haven't tried to find a way to block it. (At least I'm not paying a subscription for that part of it.)
Then of course, there are those cameras out there which cannot function as an IP camera, and are locked into only working with a cloud service (usually subscription-based). I'm assuming things like the Nest camera and the Ring doorbell camera are in that category, though I haven't looked closely at them.