In general, you do not need to bring a UK ETA printed copy or digital copy to the airport as a required travel document.
A UK ETA is digitally linked to the passport used in the application.
This means that airlines and UK border authorities can usually check your UK ETA status using your passport details.
However, it may be helpful to save your approval email or application result screen for your own reference, especially during airline check-in or travel document checks.
The most important thing is to travel with the same passport you used when applying for your UK ETA.
Before traveling, make sure your passport number, passport expiry date, and UK ETA approval information all match correctly.