Simply put, Syndicate is a fund splitting contract. The Syndicate splits fees (MEV and tips) into half and distributes them to the node runner’s smart wallet and the MEV Staking Pool.
Before even the funds (fees, tips, network rewards) are credited to the smart wallet, it goes through the Syndicate which splits the funds into halves. The first half goes to the MEV Staking pool and the other half goes to the smart wallet.
Whatever is credited to the smart wallet is the node operator’s share of the validator.