Is it possible to run both bitcoind and bitcoin-qt as backend and frontend? Multiple instances of bitcoin-qt store the blockchain data separately causing lots of waste of storage and network.

I'm thinking of running bitcoind as a local server which stores the blockchain and each bitcoin-qt as a client that handles only the wallet data and connects to the bitcoind when needed, so that users don't need to wait until the chain is synced whenever they run bitcoin-qt.

Is this configuration possible? Ive read docs saying bitcoind and bitcoin-qt shares common sources but found no further instructions.
No, you cannot do that. Bitcoin-qt is not just a frontend GUI or wallet handling software. It is bitcoind with a GUI. It does all of the same functions as bitcoind as it is built from the same sources. bitcoind also has the same wallet handling components as bitcoin-qt. bitcoin-qt has the same node, consensus, networking, etc. handling code as bitcoind.