How does public address "know" private key?
How does public address “know” private key?

It doesn't. There's no need.
When receiving money, nobody needs to know anything from you other than your receiving address (in reality a Bitcoin script, the most common types of which can be displayed as an address). At this point no-one cares about your private key.


If later wanting to sell the Bitcoin,

When spending money, you have to provide proof that you know the private key corresponding to that receiving address, without revealing the private key. This is what your wallet does when constructing the transaction details that are sent out for miners to pick up.
Other Bitcoin nodes (wallets, miners etc) can mathematically check that the proof matches the public key and will then know that you have the secret number known as a private-key.

See

https://en.bitcoin.it/wiki/Elliptic_Curve_Digital_Signature_Algorithm