As there was nothing in the owner's manual regarding stoves not lighting, I googled the symptoms and a common reason for Samsung stoves that kept popping up was the igniter failing to work, and the key identifier was the resistance value of a failed igniter being too high.
I then watched a video on Youtube on replacing the igniter and saw that it was a simple 1/2 hour procedure, and that I could get a replacement part on line from Amazon1
Before I received the part I opened up the stove to uncover the igniter and watched it in operation. The igniter glowed a dull orange and the stove didn't fully light (which matched the operation of the oven that was I seeing).
Once I received the part I removed the failed igniter as per the video2 and measured it as around 220 ohms. In comparison I measured the replacement igniter as around 100 ohms.
Once the new part was installed I tested the oven before re-installing all the cover plates. This time the igniter glowed very bright, the gas eventually started to flow3, and the oven burner lit up. After replacing everything else the stove once again worked as expected.
Here is the igniter in question. It consists of a (black) metal cage holding a ceramic block that holds the (black) heater element.

Note that the broiler uses a separate igniter (but of the same type). However, from videos I have seen you need to pull a lot off the back of the stove in order to access it. The sad part is that the broiler igniter will fail in the same manner, and that I'm probably going to have to replace it sometime in the future as well.
1. I went with a non-genuine part as it was 1/3 the price of the genuine one, plus I saw one comment from someone that said they ordered the genuine part, but was shipped the non-genuine one.
2. And the 1/2 hour project turned into a 2 hour project because I stripped the head of one of the two screws holding down the stove burner gas pipe. I went and bought a small screw extractor (that didn't work) and ended up drilling out the screw head.
3. Based on the operation I saw, the igniter does two jobs. The first is to heat up the system to convince the stove to release the gas, and the second is actually ignite the gas (after which the burning gas takes over). With a dull, glowing igniter I think that it was heating the system up to the point that was borderline for releasing the gas