I have tried searching for this answer but I must not know the right keywords or something because I can't find an explanation anywhere.
There are 2^96 addresses per private key and ~865,000,000 transactions.
If I have a private key and want to recover my transactions, it would seem that I would have to either scan the ~500GB Blockchain to see if any of my addresses are used, or if any of the transactions were encrypted by my private key.
Even if I had the Blockchain on my local machine, this would be an incalculable amount of math.
With wallet software, like electrum, where I don't have the Blockchain stored locally, I don't even see how it is possible.
Yet somehow, if I put my private key into wallet software it is able to recover all of my transactions.
How does it technically work? When I use a wallet like electrum, does it have to send my private key to some super computer somewhere?