I would recommend taking a crack at some frameworks and engines while simultaneously reading up on how games work (in general, as there are no hard rules).

Broadly speaking though, games are basically control systems. It's one big loop where the output of the previous loop affects the state of the next loop.

Modern engines and frameworks schedule the game updates and rendering separately to provide better/consistent frame rates.

Some engines I'd recommend checking out:

• https://ebitengine.org/
• https://godotengine.org/

From a programming point, SDL 3 is a good starting point, if you are doing C or C++.
It is not a game engine in itself, but a library that can help make an engine or a game directly (you don't really need an engine), so it is as "from scratch" as I would recommend going. Furthermore, it is also made to directly support Vulkan, OpenGL etc, so you can try those out.

The +ive part of that is, you are not attaching yourself to any particular engine and you can use it to understand the underlying concepts behind game programming.
The -ive is that you can't claim being experienced in any particular game engine, so the job boards asking for "Unreal Engine Developer" or "Unity" developer are inaccessible.

Another point of game programming is that it also has use in making stuff like simulators and that is where the real money lies, if you are willing to work for the military.