How can I have a second alias for a node to be displayed in a different view mode?
There are many approaches in aliasing and routing, but I think splitting the task between both is the most effective:

Add an internal node route for the second view mode:

mymodule.custom_node:
  path: '/node_custom/{node}'
  defaults:
    _entity_view: 'node.custom_view_mode'
  requirements:
    _access: 'TRUE'


Then change the source path to /node_custom/123 before Pathauto saves the second alias in hook_pathauto_alias_alter().