The Proactive Recovery (PR) mechanism in Software-Defined Networking (SDN) provides good failure recovery resilience for the Beyond Fifth-Generation/Sixth-Generation (B5G/6G) delay-sensitive applications. However, PR’s fixed single backup path policy for any flow and fine-grained backup forwarding rule configuration poses severe challenges for post-recovery congestion management and limited Ternary Content Addressable Memory (TCAM) space in SDN switches. To this end, we propose K-backup, a load- and TCAM-aware multi-backup fast failure recovery scheme for SDNs. Firstly, K-backup formulates and solves the congestion-aware multi-backup path planning problem for various failure scenarios, exploiting the inherent load diversity of multi-backup paths to minimize the post-recovery maximum link utilization. Secondly, K-backup aggregates flows sharing the same backup-path-weight pair on a link into a cascading table of Fast-Failover and SELECT groups. Meanwhile, each outputted backup path is labeled, and a corresponding label-matching flow table is configured for each intermediate switch to aggregate all flows on that path. Thirdly, K-backup dynamically adjusts the backup path update period based on the network load stabilization to reduce unnecessary controller overhead. Compared with state-of-the-art, K-backup achieves the lowest controller overhead, the best load balancing performance, the near-fewest TCAM space usage, and the near-shortest recovery time.