Dead trees keep surprisingly large amounts of carbon out of atmosphere

I'm very confused by this -- does the rate rate of carbon release matter more than the total volume? Won't the carbon in the trees eventually be released, just on a slower timeframe.

I'm not sure what you question is getting at, but yes, the carbon will eventually be released from any wood. If wood-as-carbon-storage was going to be actively applied towards climate change, then it would be important to control the rate of released, by, for example, using the wood in buildings, burying it, or submerging it in water, so that it wouldn't decompose from fungus or termites.

Sure, but it being delayed still matters a lot, particularly if it's "renewable" in the sense that trees falling into streams and being preserved underwater will be replaced over time by other trees that fall into that water on top of them.

It's the same logic for construction materials. A house has dozens of trees worth of lumber in it, and that carbon is now trapped in the house for however many decades it takes until the house eventually burns down or rots. Meanwhile the trees that were cut regrew, so the total "inventory" of trapped carbon has increased. (Appreciating of course that the lifetime carbon cost of the emissions required to maintain and climate-control a house will far exceed the modest value of what is trapped in its walls, but all of this is just for the sake of argument.)