NJ, First, nice T/A. The decals look good.
Second, I went and looked at that red one on your site ,, it definitly is still a Trans Am.
My '85 was repainted when I got it and didn't have any of it's decals but that didn't mean it wasn't a "real Trans Am"
The Trans Am package is more than just the decals. The flares and shaker hood are also a very big part of it and IIRC, you had the option to delete the decals when you bought the car. In fact, the big hood decal was always an added on option, at over $200! They even have unique serial numbers that separate them from base Firebirds and Formulas.
You could get the engine and suspension under a Formula but the hood was different [except for a few '74/'75 SD455s] and they didn't have the wheel spats and vents on the front fenders.
Here's a link to a site that will cover the basics.
https://tran-zam.com/index.html