Hello @gerry.mletzko,
Looks like the article you linked to is utilizing a NucleoL4 board (the Nucleo-L476RG to be specific) rather than an H7 board. It doesn’t really matter though, because the answer that follows applies to both. I just want to make sure we’re on the same page.
The CMSIS library is a more generic API that abstracts operations applicable to any MCU utilizing an Arm Cortex-M or Cortex-A processor. The peripherals surrounding the core in a particular MCU are implemented by the chip vendor (STMicroelectronics in this case) and thus are not generally supported by CMSIS. Looking at the structure of the various CMSIS components below, we see the oddball category called Peripheral HAL (Hardware Abstraction Layer) that interfaces with specialized peripherals (i.e., the ADC, DAC, timers, etc.). This HAL library will be supplied by the chip vendor. Note that while a CMSIS-Driver component does exist for interfacing with common communication peripherals (e.g., USART, SPI, USB), it does not appear to be supported by ST.
If you are using STM32CubeIDE to create and develop your project (as is done in the article you linked to), the STM32 HAL for your selected MCU should automatically be downloaded, included in your project, and available for you to use in your code. Shawn Hymel has another article, Getting Started with STM32 - Working with ADC and DMA, as an example of using the HAL to get samples from the ADC peripheral. Note that you can also download the ST MCU package separately as a zip file (the STM32CubeL4 package, for example) and explore all of the available drivers and example projects manually. If you do so and navigate to STM32Cube_FW_L4_V1.17.2\Projects\NUCLEO-L476RG\Examples\DAC, you will find two example projects in which the HAL is used to interface with the DAC peripheral.