My NYC era Rambler had these kinds of splits and water didn't hurt it. I didnt' try the washing machine but I imagine on delicate cycle it can't be much different than a long soak in a sink would be. along the seam edges like in your first photo I've taken a tiny amount of leather safe glue found at a fabric store, and have inserted a little bit in and let it dry into its proper shape just to add some extra protection to that delicate area.Here is some pictures of the damage:
split on strap-
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split at buckle area-
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split at other buckle area-
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Very small wearing away on piping-
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The buckles on this bag are VERY heavy an I think the leather got too dried out and then wore down in that area. I don't think I will ever get this bag back to pristine condition, but those stained areas are still noticeable after the bath.