Based on your comments, I think you misunderstand DHCP relay agents and DHCP Option 82. I will explain this below.
You need to understand the difference between layer-2 (MAC) addresses and layer-3 (IP) addresses, and how they are used.
Layer-2 addresses are used on a LAN to deliver frames from one host on the LAN directly to another host on the LAN. Layer-2 frames have source and destination layer-2 (MAC) addresses. A host sending to a host on the same LAN will use the layer-2 (MAC) address of the destination host as the destination layer-2 (MAC) address, and the layer-2 protocol (ethernet) will deliver the frames directly to the destination hosts. A host sending frames from one LAN to another LAN will use the layer-2 (MAC) address of its configured gateway (router) as the destination layer-2 (MAC) address. The sending host knows nothing about how ethernet does this (via direct connection, switch, hub, or anything else); it only knows that it sends frames out its interface. That means the host is ignorant of any switches or switch ports on the LAN.
Layer-2 (MAC) has a special broadcast address (ff-ff-ff-ff-ff-ff) that means the frames with that address are delivered to all the hosts on the LAN. a DHCP Request uses that broadcast address as the destination layer-2 (MAC) address, so every host on a LAN, including the DHCP server will receive it. Layer-2 frames only exist on the LAN on which they were originated (explained below), so this presents a problem for broadcasts, including DHCP requests, because they cannot be sent from on LAN to another LAN. That is why DHCP relay agents and DHCP Option 82 were created.
Layer-3 addresses are used to deliver packets from one LAN to another LAN, and they have layer-3 (IP) source and destination addresses. When a router receives a layer-2 frame with it layer-2 (MAC) address, it will strip off and discard the layer-2 frame, including the layer-2 (MAC) addresses, to expose the layer-3 packet. The router will look at the layer-3 (IP) destination address and compare it to the destination networks in its routing table. If if finds that the layer-3 (IP) address matches one of the networks in its routing table, it will send the packet to the next interface, and it will build a new layer-2 frame for the protocol of the new interface, which may, or may not, use MAC addresses, but the layer-2 addresses for the new layer-2 frame will be for the new interface; all the previous layer-2 frame information was discarded.
When a host sends a DHCP Request, it is sent to the layer-2 (MAC) broadcast address in the frame, and the layer-3 (IP) broadcast address (255.255.255.255, which is not allowed to be routed) in the packet. If the DHCP server is on the same LAN as the requesting host, this works well because the DHCP server gets the request. The DHCP server will then send a DHCP Offer back to to the requesting host. Depending on how the DHCP server is configured, it can send it to the layer-2 (MAC) broadcast address, or the layer-2 (MAC) host address because it learned that from the layer-2 DHCP Request frame. This also works well if the DHCP server and requesting host are on the same LAN. No special DHCP options are needed.
The problem arises when the DHCP server and the requesting host are on different LANs. DHCP is broken because they cannot broadcast to each other, and the requesting host's layer-2 (MAC) address is no good on the DHCP server's LAN. In fact the requesting host's layer-2 (MAC) address would be stripped at the first router.
To solve this problem, DHCP relay agents were created. The DHCP relay agent is configured on the router's LAN interface. The router will receive the DHCP Request because it is sent to the layer-2 (MAC) broadcast address. The DHCP relay agent is configured with layer-3 (IP) addresses of one or more DHCP servers. That is because the DHCP servers are on other LANs. The DHCP relay agent will take the broadcast DHCP Request and package it into a layer-3 packet and send it to the LANs where the DHCP servers are.
The next problem arises when the DHCP server needs to send back a DHCP offer. It would normally send it to the layer-2 (MAC) broadcast address, or the layer-2 (MAC) source address seen in the DHCP request frame on the DHCP server's LAN, but that is not where the requesting host is. That will not work because the requesting host is on a different LAN. This is where DHCP Option 82 comes in.
DHCP Option 82 allows the DHCP relay agent to tell the DHCP server to send the DHCP Offer back to it, instead of trying to deliver it on the LAN where the DHCP server is as it normally would. That is the circuit to which you refer in your comments.
As you can see, DHCP works well when both the DHCP server and the requesting host are on the same LAN, and DHCP doesn't require a DHCP relay agent or DHCP Option 82 in that case. DHCP relay agents and DHCP Option 82 were later added to DHCP as a way to centralize DHCP servers on a LAN that is different than the LAN where the requesting hosts are. Using a DHCP relay agent and DHCP Option 82 when both the DHCP server and the requesting host are on the same LAN is pointless, and they actually add unnecessary complexity to the DHCP process, but they are essential for the situation when the DHCP server and the requesting host are on different LANs.
Edit:
Consider this scenario:
I would like my DHCP server to assign IP addresses to clients based on
what port the client is connected. If the client is on port 1 I would
like it's IP to be 192.168.0.1, the client connected to port 2 should
get 192.168.0.2, and so on. Now we need information from the switch.
This can be done by SNMP, but that would probably be slow. So what if
the DHCP DISCOVER message contained the port? Yes, that's where Option
82 comes to play. The Circuit ID could contain the port. And that is
what switches do. The switch inserts Option 82 in the DHCP messages
and forwards the messages to the DHCP server.
As I explained in my comments, a switch is a transparent device, and both the DHCP server and the hosts connected to the switch are unaware of the switch or the switch ports. That is not how DHCP server work, and DHCP is not assigned as you would like, and if you were to move a host from one switch port to another during its DHCP lease time, it will still get the same IP address because it is based on its MAC address.
DHCP uses scopes as pools from which to choose IP addresses to assign to MAC addresses. Since the DHCP server and hosts are ignorant of even whether or not a switch is used, you cannot have DHCP assign addresses using the method you would like.
If your concern is knowing which IP address is assigned to which switch port, you can find that information by comparing the DHCP MAC/IP address assignments (tells you which IP address is assigned to which MAC address) and the switch's MAC address table (tells you to which switch port a MAC address is connected).
