For those wondering if the monitor runs full iOS or iPadOS, I would say the likelihood is near zero that it does. If you notice the build numbers for iOS and iPadOS, they are the same, yet they have very different features and UI’s. The builds are done at the same time, but the installer includes different files, including only the ones necessary for the device. What makes up these OS’es is a Unix kernel and file system plus libraries that run various features. iOS contains certain libraries as does iPadOS but they are not necessarily the same libraries. Sure there are overlaps, but they are not the same OS. The same goes with macOS, though it has a different build number system, probably because it is built on a different release cycle. It has vastly different libraries from iOS yet they share a common kernel.
The display monitor has the same kernel and file system but probably has a significantly stripped down list of libraries it requires. I seriously doubt the software in the monitor contains most of the libraries contained in iOS, but will contain the same libraries required to run the webcam and spatial audio. Everything else would be stripped out.
For those who comment on the size of the updates, the update size does not tell you much. All it says is that the OS files that are updated add up to a certain size, but not all files in the OS are updated each time. Someone commented their update file was 609MB. That could be the entire OS or just a subset that make up the difference between 15.3 and 15.4. There’s no way for us to tell.
Those wondering if the monitor can somehow be hacked to run applications or to use a stylus or something else, the answer is almost certainly no because the necessary libraries for running those features that would be present in iOS or iPadOS are not going to be present on the monitor. Apple would be wasting space if they included unnecessary files.
Every piece of hardware with any type of functionality has some sort of basic OS along with storage space for the firmware. It might be stored on an SSD or an EPROM. Without tearing down the monitor, we wouldn’t know. Every piece of hardware with functionality (could be a toaster, a microwave, a washing machine, a car, or a TV, etc) has a CPU, storage, RAM, and firmware that operates the hardware. Just because this one looks like iOS doesn’t mean it is the full iOS. The build number does hint that firmware updates for the monitor might be on the same release cycle as iOS/iPadOS. Likely Apple did it this way to make development easier. The monitor shares functionality with iOS, so it’s easier to just re-use code.