H Brucei, and welcome to the forum!
I would say this is for an Officer who served at sea. Coastal Artillery Officers wore grey.
Nice looking tunic and I like how the insignia has aged.
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From pages 174 & 175 of the Angolia/Bender Kriegsmarine Uniforms & Insignia (Volume 1) under "Career Insignia Of Officers" :-
Officers on the active duty list and of the body of reserves were categorized into main branches (Laufbahnen) or corps specialties.
The insignia of the respective careers were worn on the lower right and left sleeves positioned above the rank stripes, on the
shoulder boards (except sea officers), and on the field of epaulets.
The career sleeve insignia were either hand-embroidered of gold wire or machine-embroidered of yellow thread on an oval of navy
blue badge cloth. Where appropriate, the heads of insignia always faced forward e.g. head of the snake of t he medical career facing
to the wearer[s front.
The insignia were worn on the sleeves of the reefer jacket, frock coat and the blue mess jacket.
On page 177 of the same volume there is the same patch (not in bullion though, and on a field grey backing), which states:
"Coastal Artillery Marineartillerie. (Specimen is machine-embroidered on field-grey)"
And also in volume 1, page 155 there is a range of officers shoulder board career insignia shown, and the same insignia
in metal is described as "Naval Artillery"