I've got a new laptop that has the Intel Core i5 8350 processor in it and I was wondering if these new chipset still support legacy PXE boot or is it strictly UEFI.
This has absolutely nothing to do with the processor or the chipset. It depends upon whether a particular motherboard and its BIOS supports your processor and, if it does, whether it then supports UEFI PXE boot, Legacy PXE Boot, both or neither. We cannot help you answer these questions. You must contact the motherboard's manufacturer to get this information.
In your case, you know the answer to the first question but not the second. Regardless, you need to contact your manufacturer.