hook_theme_suggestions_HOOK is the one you should implement.
When you have a node of type page (labeled as Basic Page from the default profile), then the HOOK is node and the specific hook you would implement is
As @pinueve points out, there is already a specific suggestion that includes the custom display mode:
Also, as @pinueve suggests, the easy way to find the template suggestions is by enabling the debugging mode. I tested this using a custom view mode called
customvm that I created, so I can see these suggestions in the browser by inspecting the source code:
Note that there is also an alter version of the hook
[HOOK_theme_suggestions_node(array &$suggestions, array $variables)], you should use this if you are trying to alter the existing suggestions, maybe changing the priorities.
Suggestions for a page from a custom controller
The page HOOK is meant to be used when the output comes from a custom controller and route, like the one in this example:
In this case the HOOK is page and you would implement these hooks:
HOOK_theme_suggestions_page_alter(array &$suggestions, array