Keeping a laptop awake costs something: the screen and the processor stay powered. The extension's own activity costs almost nothing, so the real question is what else stays on.
What actually drains the battery
- The display. By far the biggest draw. Dim it manually even if the screen stays on.
- Background work. Syncing and heavy tabs matter far more than a little simulated activity.
- Heat. A laptop asleep in a bag is cool. One awake in a bag is not, so don't pack it while it's running.
A sensible setup
- Plug in whenever the job will run longer than your battery comfortably lasts.
- Lower the brightness and turn on battery saver where it won't slow the task.
- Close tabs you don't need, so the browser does less while it waits.
- Pause the extension when you're finished. A screen that's still being held on is wasted charge.
The lid
Closing the lid sleeps most laptops regardless of what's running. If you need a closed-lid session, that's a power-plan setting in Windows, and it's not something a browser extension can change.