Tidy setup of Python-based tests

Our Python-based system test scripts contain a lot of copy-pasted code, a lot of which does not even fulfill its intended purpose. Time to change that! Commence spring cleaning!

Note for potential reviewers

Please do not be intimidated by this:

$ git diff --shortstat origin/main
 25 files changed, 243 insertions(+), 678 deletions(-)

This merge request hardly adds any new logic. The mildly concerning 243 insertions(+) above stem mostly from moving around code in the statschannel system test without any changes to its contents. All changes are also thoroughly explained.