Why doesn't the "Remaining" field and the progress percentage update when I change the tracked time?
The progress percentage is calculated from the "Estimate" field and the "Remaining" field. And the "Remaining" field is completely separate from the tracked time in the "Used" field. So, if you change the tracked time in the "Used" field, this doesn't mean that the "Remaining" field or the progress will update accordingly.
For example, if you've done 2 days of work on a task, but have realized that the task will take longer than expected, the "Remaining" field should maybe only be reduced by 1 day of work. Because of that, you must edit the "Remaining" field separately from the tracked time in the "Used" field. They are not tied together, since that would make it impossible to register that something took more or less time than estimated (which is the main purpose of the time tracking in the "Used" field).
In other words, you should think of the "Used" field as a way to track how much time you have spent, for billing of customers, internal accounting, or checking the accuracy of your estimates. And the "Remaining" field is what is used for the tracking of progress, burndown, and whether you are ahead or behind as shown in the Sprints page. Sometimes, the amount of time you have used doesn't correspond exactly to how much progress you have actually made, or your estimates may have been inaccurate, which is why the "Used" and "Remaining" fields are not synchronized automatically.