The cord or whatever it is under the agitator is probably just something wrapped around the agitator drive shaft. You may have to pull the agitator to get it out.
I doubt it is related to the leak.
Since it only leaks during the drain cycle those parts that carry water during drain are the ones you want to check.
Hi. I looked around in inside the washer and couldn’t find any indication of the model. The space is quite compact, so it difficult to pull it out to look further.
What are the parts that carry water out during draining so I can look into it more? I’m quite a novice in terms of repairs.