But if I extract the private keys of all 7 addresses and individually load one by one address then server will not have any knowledge that all 7 addresses were a part of the same HD wallet.
To add to o_e_l_e_o's reply:
You should also generate your seed phrase and extract the individual private keys (and addresses for watch-only wallets) on an offline device.
If your HD wallet has connected to a server, your privacy has been already compromised.
How the online existed blockchain already figured out the wallet address belongs to an offline wallet that is already created?
The blockchain explorer can't know whether your address belongs to a hot wallet or an offline wallet at all and if you use TOR connection, they won't have any way to link your addresses to your IP addresses.
But if you search for multiple addresses in a block explorer in a short time, they will probably conclude that there's a connection between those addresses.