| The browser https://dev.openwrt.org/browser is not only to look at the source code without actually downloading it, but mainly to document changes. If, for example you suddenly miss the packages
You can always download the code and watch it in your favorite editor. If you merely want to have a look at it, there is software to make this experience very comfortable: OpenGrok, LXR Cross Referencer, etc.
You can also read about changes without having to look at the source code:
Sadly there are some basic articles only, regarding this very interesting possibility:
There is a own independent project concerning itself with this matter, it's called Freifunk. They also provide some modified OpenWrt version for this purpose, but it is based on an old OpenWrt release… (( It's supports cheap but old hardware, and many newer devices are not supported at all ((