Hello, I think this might be official, although I am not 100% confident about that. The portrait does look a bit basic compared to some other portraits from Trier, but the lettering of the remaining legend and mintmark as well as the reverse style make me think it's official. Here is an example of the same reference that is pretty close in terms of style : https://www.nummus-bible-database.com/monnaie-81966.htm
I doubt it’s barbarous. Looks official to me. Although barbarous is a somewhat tenuous term sometimes, I don’t see the abstract/crude nature evident in most barbs
The style looks authentic rather than barbarous. These are plentiful and quite cheap. I have several. I will try and dig out some photos.....
Here are three of my examples. I dug them out and took some photos as they had never been photographed. Two of mine are TRP Crescent and one is TRS Crescent like yours.
Here is an example from my collection that IS unofficial/ barbarous. The Obverse is very well executed, the Reverse gives it away though.
I believe that it is almost certainly barbarous. The quality of engraving is good and the reverse is fairly close to standard design, but the obverse has a poorly proportioned head - far worse than the normal range one would expect for an official issue. In addition, the type (GE 1-standard) and Trier mint mark are among the most copied. SC PS tenbobbit, your coin also has a blundered obverse legend. Very nice.