Comment # 1 on bug 1226397 from Andreas Stieger

You have not reported what you did to trigger the message, that is usually
needed to assist.

These packages seem to be fine:

zypper search -t package -s --match-exact libvulkan_intel
Mesa-vulkan-device-select
Loading repository data...
Reading installed packages...

S | Name                      | Type    | Version      | Arch   | Repository
--+---------------------------+---------+--------------+--------+------------------------
  | libvulkan_intel           | package | 24.0.8-377.1 | x86_64 |
openSUSE-Tumbleweed-Oss
  | Mesa-vulkan-device-select | package | 24.0.8-377.1 | x86_64 |
openSUSE-Tumbleweed-Oss

There is also a valid solution installing them:

$ zypper in --dry-run libvulkan_intel Mesa-vulkan-device-select
Loading repository data...
Reading installed packages...
Resolving package dependencies...

The following 2 NEW packages are going to be installed:
  Mesa-vulkan-device-select libvulkan_intel

2 new packages to install.
[...]

The message that you see is informational, for you. You as the user need to
resolve it. Please run "zypper dup" to resolve the conflict interactively. You
will be offered choices.

Closing as WORKSFORME, as performing an interactive conflict resolution using
"zypper dup" is the overwhelmingly likely solution. See bug 1225965 for the
Discover usability issue.