Do long-term fuel-trim readings represent one overall correction or change with the active airflow and load cell?

They're tied to where the engine is operating, not one global number. HP Academy explains the mechanism:

• Short-term trim is the instant correction for an error happening right now, such as running rich against the target.
• Long-term trim: if a short-term correction persists at a given operating point, the computer decides the calibration is wrong at that point and learns a long-term correction there. That lets the short-term trim return toward zero.

So long-term trims can differ between idle, cruise and other load/airflow areas. HP Academy's target is trims as close to zero as possible — within about ±3%, with up to ±5% tolerated. See tuning fundamentals.

Want to do it yourself? See who tunes it, and how to learn.