I have an old house (built in North Dakota in 1946). When my washing machine (located in the basement) was draining earlier today (high temp of 0° outside - not that cold temperatures ever caused this issue before), the "laundry" floor drain it drains into wasn't able to take in as much water as the washing machine was dumping, so a small area of my utility room flooded. That flooded water would've normally drained into my "emergency" drain (idk what it's called but I assumed it was there in case of any general basement flooding), but that appears to be clogged too. When I used my basement toilet, shower, and sink (which are 15 feet away from these two troublesome drains), they worked fine. When I ran the shower and sink, I didn't see a rise in the laundry or emergency drain water levels. From what I gathered from chat gpt, my main sewer line isn't clogged, but the piping connecting the laundry and emergency drains to my main line may be. I tried gently persuading a 1/4" drain snake, but I couldn't grab anything nor could I get the snake to travel perpendicular. The only thing I see besides water is corrosion, rusty flakes. When I looked in the emergency drain, I found a 2" PVC plug loosely laying (see picture for drawing where I found it). The plug was hidden and was very easy to take out (no twisting, just lying there). Any ideas what is going on? I would greatly appreciate any advice. Thank you.

Help please. Basement floor drain clogged?