This issue is still present in the latest 6.5.0-21-generic kernel.

/var/lib/dkms/r8168/8.049.02/build/r8168_n.c: In function ‘rtl8168_set_mac_address’:
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24197:19: warning: passing argument 1 of ‘__builtin_memcpy’ discards ‘const’ qualifier from pointer target type [-Wdiscarded-qua
lifiers]
24197 |         memcpy(dev->dev_addr, addr->sa_data, dev->addr_len);
      |                ~~~^~~~~~~~~~
./include/linux/fortify-string.h:648:27: note: in definition of macro ‘__fortify_memcpy_chk’
  648 |         __underlying_##op(p, q, __fortify_size);                        \
      |                           ^
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24197:9: note: in expansion of macro ‘memcpy’
24197 |         memcpy(dev->dev_addr, addr->sa_data, dev->addr_len);
      |         ^~~~~~
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24197:19: note: expected ‘void *’ but argument is of type ‘const unsigned char *’
24197 |         memcpy(dev->dev_addr, addr->sa_data, dev->addr_len);
      |                ~~~^~~~~~~~~~
./include/linux/fortify-string.h:648:27: note: in definition of macro ‘__fortify_memcpy_chk’
  648 |         __underlying_##op(p, q, __fortify_size);                        \
      |                           ^
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24197:9: note: in expansion of macro ‘memcpy’
24197 |         memcpy(dev->dev_addr, addr->sa_data, dev->addr_len);
      |         ^~~~~~
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24199:32: warning: passing argument 2 of ‘rtl8168_rar_set’ discards ‘const’ qualifier from pointer target type [-Wdiscarded-qualifiers]
24199 |         rtl8168_rar_set(tp, dev->dev_addr);
      |                             ~~~^~~~~~~~~~
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:575:59: note: expected ‘uint8_t *’ {aka ‘unsigned char *’} but argument is of type ‘const unsigned char *’
  575 | void rtl8168_rar_set(struct rtl8168_private *tp, uint8_t *addr);
      |                                                  ~~~~~~~~~^~~~
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c: In function ‘r8168_csum_workaround’:
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:27733:24: error: implicit declaration of function ‘skb_gso_segment’; did you mean ‘skb_gso_reset’? [-Werror=implicit-function-declaration]
27733 |                 segs = skb_gso_segment(skb, features);
      |                        ^~~~~~~~~~~~~~~
      |                        skb_gso_reset
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:27733:22: warning: assignment to ‘struct sk_buff *’ from ‘int’ makes pointer from integer without a cast [-Wint-conversion]
27733 |                 segs = skb_gso_segment(skb, features);
      |                      ^
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c: In function ‘rtl8168_resume’:
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:28693:32: warning: passing argument 2 of ‘rtl8168_rar_set’ discards ‘const’ qualifier from pointer target type [-Wdiscarded-qualifiers]
28693 |         rtl8168_rar_set(tp, dev->dev_addr);
      |                             ~~~^~~~~~~~~~
/var/lib/dkms/r8168/8.049.02/build/r8168_n.c:24214:26: note: expected ‘uint8_t *’ {aka ‘unsigned char *’} but argument is of type ‘const unsigned char *’
24214 |                 uint8_t *addr)
      |                 ~~~~~~~~~^~~~

Parts of the kernel have changed and the r8168 source needs to be updated for compatibility.