No, Wyze Cam Pan v4 is compatible with Wi-Fi 6, but it is not required.
You can use your existing router if you don't have Wi-Fi 6, just note these connectivity requirements:
2.4 GHz and 5 GHz Wi-Fi, Wi-Fi 6 and Wi-Fi 4
802.11 b/g/n 2.4 GHz (Does not support 5 GHz networks)
Supports WPA and WPA2 protocols
Upload speed for 2K: 3 Mbps
Upload speed for HD: 2 Mbps
Upload speed for SD recording: 1 Mbps