Yes it's the remaining stump of an old tree that's been floating vertically in the lake for a very, very long time.

I don't know if there's any real guesses as to how long its been in the water (1896 is just the oldest recorded observation) but I believe the tree has been dated to being like 450ish years old.

Trees in general take a very long time to decompose, it's not actually out of the ordinary that they're still there, especially factoring in that they would have been pyrolized by the actual eruption, and I believe the water temperatures generally being cooler also slow down decomposition. For the most part they're all just slowly sinking to the bottom of the lake.

Old Man of the Lake is still floating around Crater Lake and has been there since at least 1896.