The vector in vector packet processing has little to nothing to do with vector instruction sets (SSE/AVX, VMX, RVV, etc.). Only the very latest CPUs (and historical supercomputers) have scatter/gather instructions capable of efficiently extracting packet header fields from multiple packets in parallel and if you have a large enough batch of packets process switching the vector register file is worth it to the kernel. It's just that most kernels don't spill the userspace vector registers on every context switch because it's more common to switch back to the same thread (or an other userspace thread) than using the vector registers inside the kernel. Both Linux and *BSD can and do make limited use of vector registers inside the kernel e.g. for fast encryption/decryption because it's worth the start up cost.

If I understood the VPP design and implementation details correctly they try to reduce the amortised cache misses for a batch of packets by running all packets in a batch through each software pipeline stage before processing the next stage. This should result in very good average instruction cache hit rates and should also help with data cache hit rates because packet headers are small and can be prefetched while the forwarding data structures e.g. 1 million IPv4 prefixes and their next hops can be hard to fit into L2 data caches and won't fit into L1 data caches.

I assume a carefully tuned implementation can make further gains by dedicating cores to specific pipeline stages to keep the data caches hotter at the cost of copying processed packet headers their next stage in new (sub-)batches. The actual packet content is only relevant for a few operations like encryption/decryption and modern highend NICs have line rate crypto engines to help with IPsec or TLS.