You can probably lose the "already" as this would tend to indicate that you have been vaccinated. But if you do use it, then "already been" is better form than "been already" which sounds non-native.
"I would be scared if I hadn't already been vaccinated."
As for your other constructs:
"I would have been" refers to a situation that did not happen or is never going to happen.
"I would be" refers to a future situation which is dependent upon that conditional.
Sentence 1:
"I would be scared if I wouldn't have already been vaccinated."
Too many "would / wouldn't"s. You have already signalled that it is a hypothetical with the first would, you don't need another one.
Should be:
"I would be scared if I hadn't already been vaccinated."
Except that the "already" here suggests that you have been vaccinated. If you say:
"I would be scared if I hadn't been vaccinated" means that: you are talking a hypothetical case where you are expecting not to go, whether you were vaccinated or not, but if you did go, if you were not vaccinated you would be scared.
"I will be scared if I haven't (already) been vaccinated" means you are going, but your vaccination status may or may not be in question. You hope to be vaccinated before you go, because if you have not been, then you are not going to enjoy yourself.
Sentence 2:
"I would have been scared if I haven't ..."
Incorrect mix of cases.
It should be "I would have been scared if I hadn't ..."
Scenario 3:
"(If I had been thinking of going to that festival last year), I would have been scared if I hadn't (already) been vaccinated."
This means that it was in the past, and you didn't go.
"(If I had been planning on attending the upcoming festival this summer), I would have been scared if I hadn't been vaccinated."
This means it is in the future, but it's a hypothetical situation because you have already decided not to go.
