Intel 10Gb 82599ES has no carrier

I am unable to get my Intel 10Gbit/s 82599ES NIC running. Neither on Kernel 4.19:

$ uname -a
Linux 4.19.0-8-amd64

with built-in driver:

$ sudo ethtool -i eth6
driver: ixgbe
version: 5.1.0-k
firmware-version: 0x80000827, 16.5.19
expansion-rom-version: 
bus-info: 0000:04:00.0
supports-statistics: yes
supports-test: yes
supports-eeprom-access: yes
supports-register-dump: yes
supports-priv-flags: yes

nor on Kernel 5.6:

$ uname -a
Linux 5.6.0-2-amd64

with the latest driver:

$ sudo ethtool -i eth6
driver: ixgbe
version: 5.7.1
firmware-version: 0x80000827, 16.5.19
expansion-rom-version: 
bus-info: 0000:04:00.0
supports-statistics: yes
supports-test: yes
supports-eeprom-access: yes
supports-register-dump: yes
supports-priv-flags: yes

What I did:

$ sudo ip link
8: eth6: <BROADCAST,MULTICAST> mtu 1500 qdisc noop state DOWN mode DEFAULT group default qlen 1000
    link/ether a0:36:9f:82:92:a4 brd ff:ff:ff:ff:ff:ff

sudo ip link set eth6 up:

$ sudo ip link
8: eth6: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc mq state DOWN mode DEFAULT group default qlen 1000
    link/ether a0:36:9f:82:92:a4 brd ff:ff:ff:ff:ff:ff

$ sudo ip addr add 10.1.6.207/16 dev eth6:

$ sudo ip link
8: eth6: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc mq state DOWN mode DEFAULT group default qlen 1000
    link/ether a0:36:9f:82:92:a4 brd ff:ff:ff:ff:ff:ff

and

$ ethtool eth6
Settings for eth6:
        Supported ports: [ FIBRE ]
        Supported link modes:   10000baseT/Full 
        Supported pause frame use: Symmetric
        Supports auto-negotiation: No
        Supported FEC modes: Not reported
        Advertised link modes:  10000baseT/Full 
        Advertised pause frame use: Symmetric
        Advertised auto-negotiation: No
        Advertised FEC modes: Not reported
        Speed: Unknown!
        Duplex: Unknown! (255)
        Port: Other
        PHYAD: 0
        Transceiver: internal
        Auto-negotiation: off
        Supports Wake-on: d
        Wake-on: d
        Current message level: 0x00000007 (7)
                               drv probe link
        Link detected: no

Any ideas what is wrong here?

Edit: Also tried $ sudo ifconfig eth6 mtu 9000 which didn't do anything:

8: eth6: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 9000 qdisc mq state DOWN mode DEFAULT group default qlen 1000
    link/ether a0:36:9f:82:92:a4 brd ff:ff:ff:ff:ff:ff