Existing real-time decoders for surface codes are limited to isolated logical qubits and do not support logical operations involving multiple logical qubits. We present DECONET, a first-of-its-kind decoding system that scales to thousands of logical qubits and supports logical operations implemented through lattice surgery. DECONET organizes compute resources in a network-integrated hybrid tree-grid structure, which results in minimal latency increase and no throughput degradation as the system grows. Specifically, DECONET can be scaled to any arbitrary number of $l$ logical qubits by increasing the compute resources by $O(l \times log(l))$, which provides the required $O(l)$ growth in I/O resources while incurring only an $O(log(l))$ increase in latency-a modest growth that is sufficient for thousands of logical qubits. Moreover, we analytically show that the scaling approach preserves throughput, keeping DECONET backlog-free for any number of logical qubits. We report an exploratory prototype of DECONET, called DECONET/HELIOS, built with five VMK-180 FPGAs, that successfully decodes 100 logical qubits of distance five. For 100 logical qubits, under a phenomenological noise rate of 0.1%, the DECONET/HELIOS has an average latency of 2.40 μs and an inverse throughput of 0.84 μs per measurement round.