A network with statically configured wired hosts and an internal server or servers (e.g. in a corporate setting) would be a good example of the usefulness of setting a DNS search domain. In that situation users are then able to navigate to intranet sites/services without typing out long/complex FQDNs.

My router doesn't have the ability to add search domains (my internet provider gave me limited options on this router). The only way I can make use of pushed search domains is via OpenVPN which runs on my Raspberry Pi, which is overkill to obtain such basic functionality. It would be nice to manually add search domains to a network with NetworkManager. The nm-connection-editor does allow this, but it's a hidden GUI tool in GNOME.

GNOME is going to shut down bugzilla.gnome.org in favor of gitlab.gnome.org.
As part of that, we are mass-closing older open tickets in bugzilla.gnome.org
which have not seen updates for a longer time (resources are unfortunately
quite limited so not every ticket can get handled).

If you can still reproduce the situation described in this ticket in a recent
and supported software version, then please follow
  https://wiki.gnome.org/GettingInTouch/BugReportingGuidelines
and create a new enhancement request ticket at
  https://gitlab.gnome.org/GNOME/gnome-control-center/-/issues/

Thank you for your understanding and your help.