Hello @Jayashree,
Please find my answers to your questions:
Q1) Is the authentication of U-Boot done using SMR and CR configurations?
A1) The SMR/CR Tables may be used in the process. The details of the process are cannot be shared.
Q2) Additionally, could you clarify which core (Cortex-A or Cortex-M) is responsible for performing these configurations? And how?
A2) The verification is performed by core HSE_ M7 core as you can see here [page 3 AN13750, Enabling Multicore Application on S32G2 using S32G2 Platform Software Integration, Rev. 0, 11/2022]:

Q3) I would like to understand which of these three steps is related to the code reference in the link below:
GitHub Link to hse-secboot.c
A3) That function is part of an example, which is used to format the key catalogs or setup the secure boot, therefore it is not used during the secure boot process.
You can learn more about it in page 85 of the BSP42 user manual:

To know where exactly the function you shared is used, I would recommend adding a printk inside the function and monitor the system messages.
Let me know if this information answers your question.