I'm not aware of any research along these lines, but I suspect that all placebos are not equally effective.

It's a psychological effect, so things like price or flavor or packaging likely affect its strength.

Yea there is research into it, and you're correct

Color matters: placebo colored pills work better than white pills.

Delivery mechanism matters: placebo injections work better than pills.

Idk about price, packaging, or flavor specifically. But delivery mechanism, color, number of pills, etc I remember from a study.

The 2008 Ignobel Prize in Medicine was awarded for a paper that showed that higher-priced placebos are more effective than lower-priced placebos [0].

[0] https://en.wikipedia.org/wiki/List_of_Ig_Nobel_Prize_winners...

I think it comes from our animistic roots. Magic that calls for the sacrifice of a goat is stronger than magic that calls for the sacrifice of a flower because the former requires more dedication from the caster. It would be the same with money.