"the embedded systems"
The use of the definite article there is not appropriate - there is no one embedded platform, API or framework.
In your question the "auto generated APIs" is a particular feature of ST's STM32CubeMX framework. The initialisation sequence and API is specific to both the STM32 and the CubeMX / STM32 HAL API. It is certainly not the only API for STM32 - you could program it directly at the STM32xxxx.h defined register level, use the Standard Peripheral Library (that preceded CubeMX as ST's SDK offering), or use an alternative framework such as Mbed.
If you are targeting something other than STM32, then CubeMX is entirely unavailable to you - other vendors may provide their own proprietary frameworks - or nothing. The ARM CMSIS is an API common across ARM Cortex M devices regardless of vendor, for example. While Mbed is applicable to a wide range of ARM targets, and a higher level ecosystem than either CMSIS or CubeMX. It is most directly supported by Mbed specific COTS development boards such as ST's Nucleo series. Putting it on custom hardware is slightly more work.
If you are not using an ARM based microcontroller, then Mbed is not an option either and there are few if any cross-platform, multi-vendor frameworks or SDK for architectures other than ARM.
Essentially with bare-metal embedded systems it is most often a matter of familiarising yourself with a particular target through its data sheet and user manuals, picking a development toolchain and SDK/libraries/framework from possibly several options and running with it.
While there is no common API for all embedded systems there are common principles, techniques and patterns that are generally applicable, but certainly no common API or hardware initialisation approach. There are various general texts on the subject - online resources tend to be specific to a particular framework or architecture, as do many online courses (necessarily so, as the subject is otherwise too broad).
My advice would be to continue as you are, but be aware that what you are learning is a specific and narrow aspect of embedded systems in general and do not get too hung up on the specific and accept the general principles.
@old_timer : While I appreciate the fixing of the typos, I'll stick to British English spelling if you don't mind ;-). US spelling makes it too easy to use a Z in Scrabble than its letter score of 10 deserves - ruins the game.
my apolgies didnt realize that was a British spelling, Cortex was mangled so when I went in for that I right clicked a few more on the way.
@old_timer No problem, I'm bi-lingual - English and American ;-)
this makes sense now depending on computer, site or whatever, I have seen the z and s thing over the years and now I question the spelling of some words I thought I used to know...before computers started trying to help...bottom line is that both are right (and both are wrong)...
this may be literally the first edit of someone elses I have made, it was the Cortex typo I intended to fix...