Add current set expiration threshold to task log

Add the value of the threshold to the applicable tasks, or find a way to store the thresholds, so that it can be tracked better when changes are made to it.

The issue names no files, tests, or entry points. Start by locating the task log and the current set expiration threshold, then determine how the threshold can be recorded with applicable tasks so later changes are trackable; done means the threshold value is stored or shown for those tasks.

Written by the indexing model from the issue text.