I brought up this topic because I want more explanation,if there is any development or means outside of the public Blockchain that also stores client data to ensure more privacy.
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Yes. Transactions made off of the blockchain can be private using Lightning which is a non custodial peer to peer messaging network build on top of smart contracts on the main Bitcoin chain.
Also, transactions made on the blockchain can be made private by participating in a non custodial Coinjoin transaction. BTCPay Server's coinjoin plugin, Trezor's coinjoin account, and Wasabi Wallet are all able to turn your coins anonymous without leaving any traces behind or trusting any third parties with your data.
I also learnt about lightweight wallet that connects to full node before any transaction,why is it so.....
There's different tradeoffs for wallets:
Full node: Maximum privacy, full consensus rule validation, slow sync
Filter wallet: Maximum privacy, no consensus rule validation, fast sync
Light wallet: No privacy, no consensus rule validation, instant sync