Sorry for the delay, a context is used to group a set of blocks. So you can have block related to a CMS context, or to the admin.
So an admin block will be never used in the CMS context.
Question
What does the context means inside the configurations of the Sonata Block Bundle? What is for?
sonata_block:
default_contexts: [cms]
blocks:
sonata.admin.block.admin_list:
contexts: [admin]
Solution
Sorry for the delay, a context is used to group a set of blocks. So you can have block related to a CMS context, or to the admin.
So an admin block will be never used in the CMS context.