If being inconspicuous is the main thing, then you could try a smartphone in one of those plastic pouches that you find in outdoor shops. You can carry it around your neck, or attach it to rucksack straps or similar, and most observers would assume that's just how you carry your phone.
There are various spy camera apps that can be set to take regular pictures or video on a loop. It depends on your phone and the app how easy it is to start the video, but for most purposes it might be enough to start at the beginning of the commute and just record. Downloading/managing the files is easy, and battery life of modern phones is amazing. Quality might not be as good as a dedicated camera, but should be ok for most purposes.
As you mention commuting, I assume your main aim is to record evidence if something goes wrong, and for that the quality of a mobile phone cam should be enough. Many of the other recommendations are action cams that are meant for creating impressive vids of how you handle a difficult mountain bike trail or something, but they may not be best for everyday traffic situations. For example, I have a GoPro Hero which is great (can start video with one big button), but one limitation is that the video resolution and fps rate is so high that an SD card fills up in one or two hours (and it's bulky). High fps is important for action shots, but for traffic offences you only need a much lower fps and therefore smaller file sizes.
In any case, it's worth experimenting with a smartphone app and carrying pouch as you probably carry a phone anyway.
