How can you scan millions of things looking for one or two that have a mutation?

Back in the day there were pipetting robots and 384 well plates. Probably some smart grouping techniques to hone in on a mutation in a binary search like fashion.

But nowadays we have things like single cell sequencing, which allows you to label thousands of cells with unique DNA barcodes (not the cell itself but the sequencing library you construct to go into the sequencer), and sequence them all in a massive parallel fashion.

Basically all of molecular (and other types) biology is now "high throughput", consequently data science has become very important for biologists.

If you accidentally use the same pipette for the GMO and then non-GMO one, your chances are hugely increased...

You already had to have a selection process to establish the desired trait and determine whether it was successfully hybridized into the target.

Once you know what it is, you run the same thing on the unmodified population.