No, it doesn’t work that way for HTTPS. Public Key Cryptography is a relatively expensive operation. So the public/private keys are used to create and exchange

No, it doesn’t work that way for HTTPS. Public Key Cryptography is a relatively expensive operation. So the public/private keys are used to create and exchange a temporary symmetric encryption key. That symmetric encryption key is used to encrypt and decrypt the HTTPS requests and responses later by the client and the server. What you describe is used that way when you want to send, say encrypted emails to someone else when you have their public key.