It takes a bit of work but its in ExtensionData.Hardware.Systeminfo.OtherIdentifyingInfo of the host object (i.e. what you get back from Get-VMHost). OtherIdentifyingInfo is a collection of value/type pairs.
get-vmhost yourhostname).ExtensionData.Hardware.SystemInfo.OtherIdentifyingInfo | Where-object {$_.IdentifierType.Key -eq "AssetTag" }
(get-vmhost yourhostname).ExtensionData.Hardware.SystemInfo.OtherIdentifyingInfo | Where-object {$_.IdentifierType.Key -eq "ServiceTag" }
if the service tag isn't the same as the serial number then try
(get-esxcli -VMHost yourhost).hardware.platform.get().SerialNumber