I tagged this as a regression because it must have worked at some point.
Neither the package search installed by default from
/usr/share/firefox-esr/distribution/searchplugins/common/debsearch.xml
nor a custom one I put there even show up in Firefox, search dropdown
and preferences both.

In fact, I did strace -e file on it then grepped for 'usr/share/firefox'
in the trace and did not get a single mention ☹

This has to affect more things: dpkg -S says that…

firefox-esr: /usr/share/firefox-esr/browser/defaults/preferences/firefox.js

… so all the Debian-specific preconfiguration is also ignored. If this
includes disabling phone-home stuff, then that would not be disabled
(I did not check whether it does) which would be a security catastrophe.