I am looking for a security camera that I can use to view what's going on in my apartment, without having to use a third party website/app. I am currently using one that requires me to connect to a website based in China, and I don't really trust the parent company not to snoop.
You can always use an IP camera. Ex: http://foscam.us/
Not the best quality but it usually does the trick.
IP cameras usually run their own web server so you can just open up a browser tab and type in the camera's IP ex: 192.168.0.133 or something and you will be able to see what the camera sees. And if you get a camera that can move than you will also be able to Zoom and tilt from the browser tab.
The next step would be to set up a VPN in your apartment. I like to use OpenVPN, it has worked well for me. there are a ton of tutorials how to set one up on a RasPi 2-3. Just connect to your VPN and then go to your IP camera's page and you should be good to go.
If you only need one camera than you can use: https://www.milestonesys.com/our-products/
One camera License is free. Thats what i use and its pretty robust. Do note that you will need a computer for this. A NUC or Brix should do well, I understand that might be expensive. Thats why its not totally needed.
Not sure if there are 100% open source commercial products out there, but here is an alternative.
Would you consider to set up for example a Raspberry Pi + USB webcam combo? I've had one running for about two years now, capturing and saving a JPG image once / minute. That would cost 50 - 100 USD depending on what components are used. However the system has not been 100% reliable and every now and then I've had to re-plug the USB camera in (YMMV).
I have published bash + PHP based scripts at Github, utilizing v4l-utils. I have also blogged about it. It is internet-accessible with authentication and HTTPS encryption online on my "private" domain (just storing it on hosts files). I understand this takes some engineering effort, NAT port forwarding etc. but nothing that complex.
This doesn't provide video but it might not be needed to observe "what's going on in my apartment". I'm sure there are other solutions out there but I like building my own stuff and customize for my preferences.