What is the purpose of EEPROM in the PCIe accelerator card?
tl; dr version: the MAC address EEPROM is a means to supply a field-programmable network ID for the card. It is used only by the network hardware the card supports (Ethernet, wireless, Bluetooth, etc.) and has nothing to do with PCIe.
Using EEPROM is a time-honored way of handling this which balances having the the MAC address be non-volatile, yet allowing customization as needed during production and deployment.
The MAC address has a specific format that includes a vendor ID (OUI) and the device address.
More about MAC addresses here: https://www.pcmag.com/encyclopedia/term/mac-address
Separate and distinct from the MAC address, PCIe supports unique device serial numbers (DSNs) for each card as part of the Card Information Structure (CIS). DSNs are optional. The main use for DSN is for asset tracking of devices installed in boxes.
More about DSNs here: https://docs.microsoft.com/en-us/windows-hardware/drivers/ddi/wdm/ns-wdm-_pci_express_serial_number_capability
The MAC address would not be the same value or the same format as the DSN. The card could nevertheless use the same EEPROM to store the DSN and MAC values if the hardware allowed it, with DSN copied to the PCIe CIS, while the MAC address is copied to the networking hardware.