It works but needs firmware blobs for the CPUSaver feature, maybe it depends on the other driver (eepro100), which is missing in the libre kernel?

lspci -vvnnk

04:05.0 Ethernet controller [0200]: Intel Corporation 82557/8/9/0/1 Ethernet Pro 100 [8086:1229] (rev 08)
        Subsystem: Compaq Computer Corporation NC3134 Fast Ethernet NIC (dual port) [0e11:b163]
        Control: I/O+ Mem+ BusMaster+ SpecCycle- MemWINV+ VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-
        Status: Cap+ 66MHz- UDF- FastB2B+ ParErr- DEVSEL=medium >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
        Latency: 32 (2000ns min, 14000ns max), Cache Line Size: 32 bytes
        Interrupt: pin A routed to IRQ 20
        Region 0: Memory at febfe000 (32-bit, non-prefetchable) [size=4K]
        Region 1: I/O ports at e880 [size=64]
        Region 2: Memory at fe900000 (32-bit, non-prefetchable) [size=1M]
        Capabilities: [dc] Power Management version 2
                Flags: PMEClk- DSI+ D1+ D2+ AuxCurrent=0mA PME(D0+,D1+,D2+,D3hot+,D3cold-)
                Status: D0 NoSoftRst- PME-Enable- DSel=0 DScale=2 PME-
        Kernel driver in use: e100
        Kernel modules: e100

dmesg

[   97.081022] 0000:02:04.0: Missing Free firmware (non-Free firmware loading is disabled)
[   97.081293] e100 0000:02:04.0 enp2s4: CPUSaver disabled. Needs "/*(DEBLOBBED)*/": -2
[   97.101034] 0000:02:05.0: Missing Free firmware (non-Free firmware loading is disabled)
[   97.101214] e100 0000:02:05.0 enp2s5: CPUSaver disabled. Needs "/*(DEBLOBBED)*/": -2
[   97.102838] e100 0000:02:05.0 enp2s5: NIC Link is Up 100 Mbps Full Duplex

hwinfo --verbose --netcard

10: PCI 205.0: 0200 Ethernet controller                         
  [Created at pci.386]
  Unique ID: uy4f.gBruFhIYX46
  Parent ID: 37TO.utJYbPkKj7F
  SysFS ID: /devices/pci0000:00/0000:00:10.0/0000:02:05.0
  SysFS BusID: 0000:02:05.0
  Hardware Class: network
  Model: "Compaq NC3134 Fast Ethernet NIC (dual port)"
  Vendor: pci 0x8086 "Intel Corporation"
  Device: pci 0x1229 "82557/8/9/0/1 Ethernet Pro 100"
  SubVendor: pci 0x0e11 "Compaq Computer Corporation"
  SubDevice: pci 0xb163 "NC3134 Fast Ethernet NIC (dual port)"
  Revision: 0x08
  Driver: "e100"
  Driver Modules: "e100"
  Device File: enp2s5
  Memory Range: 0xe9201000-0xe9201fff (rw,non-prefetchable)
  I/O Ports: 0x2800-0x283f (rw)
  Memory Range: 0xe9100000-0xe91fffff (rw,non-prefetchable)
  IRQ: 11 (5295 events)
  HW Address: 00:02:a5:8e:cf:b5
  Permanent HW Address: 00:02:a5:8e:cf:b5
  Link detected: yes
  Module Alias: "pci:v00008086d00001229sv00000E11sd0000B163bc02sc00i00"
  Driver Info #0:
    Driver Status: e100 is active
    Driver Activation Cmd: "modprobe e100"
  Driver Info #1:
    Driver Status: eepro100 is not active
    Driver Activation Cmd: "modprobe eepro100"
  Config Status: cfg=new, avail=yes, need=no, active=unknown
  Attached to: #14 (PCI bridge)

13: PCI 204.0: 0200 Ethernet controller
  [Created at pci.386]
  Unique ID: Rnqa.gBruFhIYX46
  Parent ID: 37TO.utJYbPkKj7F
  SysFS ID: /devices/pci0000:00/0000:00:10.0/0000:02:04.0
  SysFS BusID: 0000:02:04.0
  Hardware Class: network
  Model: "Compaq NC3134 Fast Ethernet NIC (dual port)"
  Vendor: pci 0x8086 "Intel Corporation"
  Device: pci 0x1229 "82557/8/9/0/1 Ethernet Pro 100"
  SubVendor: pci 0x0e11 "Compaq Computer Corporation"
  SubDevice: pci 0xb163 "NC3134 Fast Ethernet NIC (dual port)"
  Revision: 0x08
  Driver: "e100"
  Driver Modules: "e100"
  Device File: enp2s4
  Memory Range: 0xe9200000-0xe9200fff (rw,non-prefetchable)
  I/O Ports: 0x2400-0x243f (rw)
  Memory Range: 0xe9000000-0xe90fffff (rw,non-prefetchable)
  IRQ: 9 (16412 events)
  HW Address: 00:02:a5:8e:cf:b4
  Permanent HW Address: 00:02:a5:8e:cf:b4
  Link detected: no
  Module Alias: "pci:v00008086d00001229sv00000E11sd0000B163bc02sc00i00"
  Driver Info #0:
    Driver Status: e100 is active
    Driver Activation Cmd: "modprobe e100"
  Driver Info #1:
    Driver Status: eepro100 is not active
    Driver Activation Cmd: "modprobe eepro100"
  Config Status: cfg=new, avail=yes, need=no, active=unknown
  Attached to: #14 (PCI bridge)