Compact Camera for nighttime live streaming? We recently adopted a pet hamster for our office, and are interested in setting up a live feed for evenings and weekends so that employees and customers can tune in to the lil guy during his most active hours, and so we can additionally make sure he's doing alright when there are not as many people in the office to check up on him.

We'd be working with close quarters here - he's in a plastic DIY hamster cage that measures 12.62 inches (H) x 18.75 inches (W) x 34.62 inches (L). Because the plastic is not 100% clear the camera would need to be mounted inside the lid of the enclosure, in a corner. We need a fairly small camera as a result, just to ensure he can't climb up to it and chew on it. (It's a dwarf hamster though, so as long as it's a few inches off of the bottom of the enclosure that should be fine... he's short!) If need be, we could probably make a hole in the enclosure for the lens to peek through, but I'd like to avoid that.

The cage currently isn't terribly close to an ethernet switch, so WiFi would be ideal, but the cage could likely be moved to be connected to either my extra Linux box via USB or directly to ethernet. I would then be running broadcasting software on the Linux box to send the stream to Twitch or YouTube or whatever works.

I don't know nearly enough about cameras to know where to start. If it could be done for under $100, that would be a great start - not looking for super high quality, just like a nanny cam situation but on a smaller scale. I've felt a little lost looking online, as it seems many of these consumer surveillance cameras all have their own specific apps you have to view the feed through, with limits, etc, and I just want to be able to access the feed directly so that I can forward it on to the internet.
You can use old(ish) Android phone to have all-in-one solution or you can use go-pro camera with laptop.