Quote Quoting JustANobody
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For the purposes of this discussion of a hypothetical, the USA is sufficient and what was said was 'the defendant is represented by the public defender' during prosecution's opening and the public defender introduced themselves the same way during their opening.
Then unless the defendant’s financial means was somehow relevant to the trial there is almost certainly no chance of prejudice in a simple statement that the defendant is represented by a public defender.

Quote Quoting JustANobody
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The prejudice resulting from the jury hearing that which is not relevant and contrary to the defendant's 6th amendment rights, is the jury panelists are paying for both sides and one might be a bit desensitized not to believe a panelist will harbor a natural bias against somebody that cannot afford counsel as opposed to a defendant that rolls in with a law firm everyone knows costs at least as much as a down payment on a home, if not a home.

I'm thinking years of outcomes reflect juries generally believe wealthy people are less likely to be guilty.
Your logic is flawed. In most trials, the wealth (or lack of it) is not presented to the jury, and there are no reliable studies that suggest that juries tend to think that wealth alone bears on the issue of guilt, or even plays any significant part in it. What you do see is that people with wealth can afford to buy the best legal services, and that better representation then shows in the outcomes that the person gets. In other words, the jury is persuaded by the good representation, not by the mere fact that the defendant is wealthy. It is just simply the fact that wealth allows a person to buy that good representation.

In most circumstances I don't see a defendant getting any traction making an issue over a statement that he was represented by a public defender.