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The destination ethernet address for DHCP can be the broadcast address (ff:ff:ff:ff:ff:ff)
or a specific device MAC address. See the DHCP RFC (https://www.ietf.org/rfc/rfc2131.txt) for info about when unicast and broadcast addresses are valid.
A switch only sends packets out a port that are either addressed to the attached device or to the broadcast address. Any DHCP packets being sent to the bulb MAC addresses won't be sent to the desktop switch port.
Moving the desktop to the router will help but you will also need to configure that port to be a Monitor port to see all traffic. Capture configuration and when to use a Monitor port are covered here: https://wiki.wireshark.org/CaptureSetup/Ethernet