No schema for my_module.global error on unit test
Turns out that it is related to the my_module.schema.yml. Looks like every YAML file under my_module/config/install must have a corresponding schema in the my_module.schema.yml file in order to set up a unit test, even if this is not actually required for the module to work. It needs to look something like this (assuming the config/install file name is my_module.global.yml):

my_module.global:
  type: mapping
  label: 'My label'
  mapping:
    property:
      type: text
      label: 'Property label'


If unsure which properties need to go there, running the unit test without them will give a list as part of the error. I'm sure there is a better way to find this, but that's the way I found so far.

Edit – the whole schema verification mechanism can be turned off: In drupal/core/lib/Drupal/Core/Test/TestSetupTrait.php, $strictConfigSchema needs to be set to FALSE.