Apparently, we were incorrectly expressing the paths in the
caches_in_use data structures for these two cache-cleaning algorithms,
resulting in the default threshhold_days algorithm controlling which
caches could be garbage-collected. While the emoji one was just a
performance optimization for upgrade-zulip-from-git, it was possible
for the main `node_modules` cache in use in production to be GCed,
resulting in LaTeX rendering being broken.
This saves about 400ms when running clean-unused-caches, basically by
calling its sub-rountines by import (rather than
`subprocess.check_call()`). The performance optimization seems well worth it.
Fixes#9766.