Do I need a managed switch for a home network?

For most homes, no. Unmanaged switches are plug-and-play and the consensus across r/HomeNetworking is that they're sufficient unless you specifically want VLANs, QoS, port mirroring, link aggregation, or integration with a controller like Omada or UniFi. If you do want those features, the TP-Link Omada ES206X-M2 is a low-cost entry point at 2.5GbE.