How would legal procedure change if every citizen eligible for jury duty was aware of jury nullification?

Everyone being aware of it doesn't mean it would happen all the time. I'm very aware of it and if selected I would still hear the case as dispassionately and impartially as possible, as I view a jury trial as a civic duty and an important cornerstone of criminal justice.
But I suspect the question you're really asking is "What if every juror refused to convict in any crime?" And the answer to that question is that jury trials would no longer be a thing if juries weren't useful. Judges would hear the cases and rule themselves (and judges already rule summarily in many trials today).
- Its actually not, I'm just curious because they obviously try to screen out anyone even superficially aware of it so it raises the interesting question of how that would play out societally, like would the death penalty leverage essentially be erased and in what other ways would it affect jurisprudence and application of the law
  
  I find it interesting that simply having been involved in litigation (I got sued once for an art piece) seems to be enough that I go home every time I'm called for jury duty. They really do want people with no idea.
  
  Have you ever been selected for jury duty? I haven't, so I can't speak to the screening process.
  In cases of capital punishment I wouldn't be surprised if they screen out people who are against it, since it would be a conflict of interest. A jury's only purpose is to determine whether someone is guilty of a crime, not to weigh in on sentencing. Although I'm pretty sure sentencing comes later anyway.
  
  I’ve been called in for jury duty a number of times, made it to the courtroom a couple of times, and was seated on one of them. None of those times did anybody ask if we were aware of jury nullification, or anything that was related to it.
- But I suspect the question you're really asking is "What if every juror refused to convict in any crime?"
  Eventually they would allow jurors to bring their guns...
  /s

Probably would make prosecutors think twice about bringing certain cases to trial. Any "sympathetic" defendants would likely just get a plea deal, and probably a lax one.
Influencers/Famous people could also do what they like, because prosecuting means risking that a jury could just side with them, regardless of the seriousness of the crime.

Supposing that any change did materialize, it is a bedrock principle of legal procedure to not change substantially just because the outcomes have noticeable changed. That is to say, if there was anything like a sudden drop in conviction rates, it would be improper for the judges, appellate justices, and defense and prosecuting attorneys to do anything different than what they would have done prior. That's kinda the point of having a procedure: to follow it and see what happens, accepting the result of turning the cogwheels.
The path to making such changes would have to be done legislatively, since -- at least in the USA/California -- that's how changes to the law and civil/criminal procedure are made. Sure, entities like the Judicial Council of California would be making recommendations, but it's on the Legislature to evaluate the problem and implement any necessary changes.
Law without procedure would just be decrees, wayward and unprincipled.

It wouldn't.
One way to check could be to get a billboard outside a court house, or as close as possible. Inform the public via the billboard. Check if court outcomes change.

Jurors would weight in feelings over facts.
Which means, yes, Mangione gets acquitted.
But also possibly acquitals the when a cop murders someone, or when a group of white men chases down an unarmed black man and shoots him.
Possibly even some mass shooters, if they were white, because they'd be viewed as a "troubled youth" rather than a cold hearted killer.
Nullification goes both ways.
And if the accused is someone the jurors don't like, its possible, with the idea of nullification in mind, they'd be more willing to just overlook the facts and convict based on "gut feeling".
Because, what adding nullification to the jury instructions is doing, is that you are instructing the jurors to become not just the finder of facts but also the finder of law.

I don't think much would change. Prosecutors already weed out sympathetic jurors during selection and a non-sympathetic jury wouldn't nullify even if they knew they could.

Far fewer than 1 in 20 defendants get a jury trial in the US. If every defendant insisted on their right to one, then the system would break down for lack of jurors.
Few juries would decide to nullify, since, by and large, Americans believe in punishment.
So the change would be insubstantial.