May I safely use Drain-o or Liquid Plumber in a dishwater as long as I rinse it thoroughly with an empty dish cycle afterwards?
I would not use either product as they will eat some plastics.

Undo the drain hose at the house plumbing and let it drain into a pail.
Be sure to hold the hose firmly and put a towel over the pail so water does ont splash all over.
Check where the hose attaches to the house plumbing this is a common place where debris collects and plugs the drain.

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Replacement parts for General Electric GSD3230F00WW Dishwasher | AppliancePartsPros.com

Remove the sump cover (center of the tub) and check it for debris or anything wrapped around the chopper. Be careful as there is often broken glass in the sump.

A common problem with these units is the piston and nut (Item 564 in Section 2). It is behind the rear filter assembly in the tub. It unscrews.
Remove it and check that it is sealing.
What happens if it does not seal correctly is that during drain some of the water goes back into the tub instead of out the drain.