I would like to know is there any elite components for Qt that can have a style like the TabControl from Adobe software (but still free for commercial use)- e.g. such that I can choose a color or style. The image below clears up what I am looking for. Standard Qt SDK controls do not satisfy my needs.

If the stock Qt widgets don’t meet your needs, you are free to customize the look of them using stylesheets: https://qt-project.org/doc/qt-4.8/stylesheet-examples.html#customizing-qtabwidget-and-qtabbar
If stylesheets still don’t provide you enough freedom, then you would simply compose your own custom widget by subclassing the closest classes and organizing them the way you want.
The tab widget you show looks like a basic tab widget with nested layouts with labels, etc. The actual colors can be accomplished with stylesheets. The angles on the tabs and frame are the only more challenging aspect, which can also probably be accomplished with stylesheet graphics, or a custom paint method for your widget.