Correct. Reduced smoking, alcohol, and other behaviors have been documented. There's a complex relationship between the gut and certain behaviors. These drugs slow down gut processing, and delay the reward mechanism. With slightly less reward from the body, the scales may tip slightly in favor of self control.

Source: currently using GLP and seeing reduced positive feedback from alcohol (incidentally)...

Once you have proven to yourself you can eat less and lose weight, you believe you can do the same with other things like smoking.

Makes sense

That's not how it works.

There is not enough evidence to say this is true.

It could absolutely be a factor in the effectiveness.

Placebo is a highly effective drug.

I say this as an extreme evangelist of GLP-1s. Behavior modification and habit building appears to me to be a large part of it. Friends on it who have used to as a performance enhancing drug to change habits have generally stuck with newly developed habits even coming off the drug. Friends who used it as a magic weight loss drug largely returned to previous weights and poor health, even some maxing out the doses over time.