You've not grasped the point.
The definitions in the OP are all about reaching a mental state known as a decision. When people talk abotu free will, they don't just talk about mental states, they talk about effective intentions. In other words, they talk about deciding to do something and then
carrying out that decision. If your definition doesn't include the connnection between decision and action, then you can't distinguish between some positions on free will. For example, both DBT and I agree that neural events known as decisions in fact occur. What we don't agree on is whether those neural events have any effect whatsoever on behaviour. You definition doesn't include that difference.
I still do not understand what people mean by compatibilist free will beyond the idea that decisions are not coerced.
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That leads me to conclude that everyone talks about free will but no one knows what it really means beyond saying that it involves contra-causal choice - the ability to choose otherwise (whatever that means).
Ok, a brief overview.
There are (very broadly) two types of free will that people argue about. They differ on how they treat concept of determinism - the idea that everything is entirely determined by prior events.
Incompatibalist (or Libertarian) free will is the idea that, in order to be free, actions must be free from external determination. That is, if your decision is entirely caused by prior external events, then you can't have free will. It uses a definition of free will such that determinism is incompatible with free will.
Compatibalist free will is the idea that, in order to be free, actions must be free from coercion. That is that so long as someone is not being threatened, physically forced, or similar, then they have free will. It uses a definition of free will such that determinism is entirely compatible with free will.
The vital point here is that it is the definition of free will that is different in each case.
The most common positions are that:
Determinism is false, libertarian free will is true, compatibalist free will is true
Determinism is true, libertarian free will is false, compatibalist free will is true
Determinism is true, libertarian free will is false, compatibalist free will is false