Maybe it was. Would that really bother you so much if we reframed it that way? As a student of history, I recall from my studies that we had a lot of military interactions with England, after gaining independence, testing it if you will and yes, these could be seen initially as potentially a Civil War if England had chosen to escalate.
Its an issue of “reframing” as a propagandistic maneuver.
Looked at as a matter of geopolitics it (the war of 1812) was a war, plain and simple, with international consequences.
The US effectively came to war in aid of Napoleon, by harassing British trade, by invading its colony of Canada, and diverting resources from continental Europe, in particular from the British efforts in Spain. Britain was stretched at the time, both fiscally and in military manpower.
The war of 1812 mattered, as the Ukraine war matters, in current geopolitics.