The safest way is running the command as a service in the system slice:
karl@3400g:~> systemd-run zypper --non-interactive dist-upgrade --download-only --dry-run
Running as unit: run-u1751.service; invocation ID: b2d4451d098e46cdb593c3b47547555e
karl@3400g:~>
Journal tells everything:
karl@3400g:~> journalctl --unit run-u1751.service --no-pager
Jun 29 10:19:17 3400g systemd[1]: Started /usr/bin/zypper --non-interactive dist-upgrade --download-only --dry-run.
Jun 29 10:19:17 3400g zypper[184436]: Loading repository data...
Jun 29 10:19:17 3400g zypper[184436]: Reading installed packages...
Jun 29 10:19:18 3400g zypper[184436]: Warning: You are about to do a distribution upgrade with all enabled repositories. Make sure these repositories are compatible before you continue. See 'man zypper' for more information about this command.
Jun 29 10:19:18 3400g zypper[184436]: Computing distribution upgrade...
Jun 29 10:19:18 3400g zypper[184436]: The following 9 packages are going to be upgraded:
Jun 29 10:19:18 3400g zypper[184436]: libvdpau_r600 libvdpau_radeonsi libvulkan_intel libvulkan_radeon Mesa-dri Mesa-gallium Mesa-libva Mesa-vulkan-device-select obs-studio
Jun 29 10:19:18 3400g zypper[184436]: 9 packages to upgrade.
Jun 29 10:19:18 3400g zypper[184436]: Overall download size: 0 B. Already cached: 124.1 MiB. Download only.
Jun 29 10:19:18 3400g zypper[184436]: Backend: classic_rpmtrans --dry-run --download-only
Jun 29 10:19:18 3400g zypper[184436]: Continue? [y/n/v/...? shows all options] (y): y
Jun 29 10:19:18 3400g zypper[184436]: In cache obs-studio-29.1.3-1699.3.pm.18.x86_64.rpm (1/9), 84.3 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache Mesa-gallium-24.1.2-1699.385.pm.3.x86_64.rpm (2/9), 11.4 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache Mesa-libva-24.1.2-1699.385.pm.3.x86_64.rpm (3/9), 4.1 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache Mesa-dri-24.1.2-1699.385.pm.3.x86_64.rpm (4/9), 8.9 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache libvdpau_radeonsi-24.1.2-1699.385.pm.3.x86_64.rpm (5/9), 3.8 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache libvdpau_r600-24.1.2-1699.385.pm.3.x86_64.rpm (6/9), 3.8 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache Mesa-vulkan-device-select-24.1.2-1699.385.pm.3.x86_64.rpm (7/9), 73.7 KiB
Jun 29 10:19:18 3400g zypper[184436]: In cache libvulkan_radeon-24.1.2-1699.385.pm.3.x86_64.rpm (8/9), 2.5 MiB
Jun 29 10:19:18 3400g zypper[184436]: In cache libvulkan_intel-24.1.2-1699.385.pm.3.x86_64.rpm (9/9), 5.4 MiB
Jun 29 10:19:19 3400g zypper[184436]: Checking for file conflicts: [...done]
Jun 29 10:19:19 3400g systemd[1]: run-u1751.service: Deactivated successfully.
Jun 29 10:19:19 3400g systemd[1]: run-u1751.service: Consumed 1.716s CPU time.
karl@3400g:~>
There is absolutely no point in using screen, tmux or others, in my opinion of course.
Users may want to tweak their systems: