task failures due to reduced PATH variable

Debusine workers inherit the PATH variable from systemd and inherit it to its tasks. In trixie, the default PATH variable dropped /bin and /sbin. Unfortunately, we are still dealing with split-/usr Debian releases such as stretch and buster. When those directories go missing, apt-key may be unhappy about not being able to find mktemp and make apt-get update fail. This presently breaks the blhc, extractforsigning, lintian, and piuparts on https://debusine.freexian.com

How do we want to deal with this? Is it the responsibility of the administrator to sanely define PATH or should Debusine be more actively supporting compatibility with old releases?