The 7th Amendment is not generally said to have any real connection to the right to privacy. The right to privacy is not actually explicitly mentioned in the Constitution. Instead, it is said to be implied by several of the amendments to the Constitution. Those amendments protect rights that have to do with keeping a person’s affairs private and unregulated by the government. The 7th Amendment is not one of these amendments.
The 7th Amendment only has to do with trial by jury. More specifically, it guarantees a trial by jury in any civil case where the amount of money at stake is more than $20. This does not really have to do with privacy.
The right to privacy comes more from amendments like the First, the Fourth, and the Fifth Amendments. These Amendments protect people from having the government interfere in their private lives. A jury trial does not prevent the government from doing this. Instead, it is meant to prevent the government from treating you unfairly once you have already been brought to trial.
Thus, the 7th Amendment really does not have to do with the right to privacy.