I don't know if that is intended. You could report a bug.
If you do not have a full backpack, is the menu still cut off? The storage conflict warning tends to stretch the dialog.
I'm having trouble submitting the report... It's saying the issue could not be loaded.
I think it doesn't. The storage conflict does extend the message.
The issues tracker ... has issues. See this explanation of how to know you're submitting a valid issue.
This isn't just the cobra I don't think; when there is a backpack conflict it increases the height of the dialog, versus having room for backpack contents.
I have a Fer De Lance and a Cobra MK III: The menu options don't cut-out on the boarding menu like it does in the Cobra MK V (when I board it with a Storage Conflict warning). This is definitely something isolated to the Cobra MK V.