I guess the short explanation would be that être is a verb-of-state (verbe d'état). And those verbs are overwhelmingly used in the imperfect tense since they describe a state and not an event. Here's more on this: https://progress.lawlessfrench.com/questions/view/what-are-verbes-d-etat-s-il-vous-plait
The French sentence is in the primary language, and therefore is ‘correct’, by definition.
Regardless of whether the French was in imparfait or passé composé, a natural English translation could be “You were late this morning”.
“…. running late… ” is an English alternative for the translation of the imparfait here, but may have been more confusing as there is clearly no reference to ‘running’ in the French sentence ! If you asked a French native speaker to translate from ‘You were running late this morning’, you could very well get ‘ Tu courais tard ce matin ‘.
Generally, être will be used in imparfait - and in this case, although the ‘late’ clearly occurred in the morning, there is no specific time for the event itself - it has vague (unspecified) time boundaries - paradoxically perhaps, I do think this becomes clearer when we think of it as ‘running late’ in English.
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