I found out this is not a fern. It's in a different plant family. It's just called a foxtail asparagus fern because the fine-leaved needles look similar to asparagus fern. Oh well, I like the funny plant anyway.
I've been watching mine put out long new shoots. First it's a plain slender stem
Then tiny little leaves start to unfold.
When the needles first emerge along the side stems they mostly point in one direction. But when the entire 'plume' is filled out, it actually has an interesting spiral growth habit. So far I have been unable to get a photograph that shows this, it's a very subtle thing and hard to see in the dense, fine foliage.
When I bought this the nursery worker had told me it was okay to cut off these fat storage roots when repotting, they'll grow back, but I was loathe to do so. I cut a few and cut out the drainage holes to work the rest of them out of the pot. I knew it needed repotting, but hadn't realized how bad its condition was. I'm glad I looked up the plant care, and found out it's actually a tough one, can withstand some neglect and that's a good thing, mine sure was neglected. When the needles turn yellow it's thirsty, brown if it's waterlogged. I found this out after noticing mine had a few of the lower plumes gone yellow and dry.
I was shocked how incredibly dry and rootbound the poor plant was.
I put it in a bigger clay pot. Already note that when it recovers, will need potting up another size again soon. It has more extra room in the base than on the sides, here. Its square shape just fit into the round pot, so I wasn't yet able to straighten out the lopsided orientation.
Here you can see how fine the needles are. Pictured next to some nicotiana seedlings, which are some of the smallest seedlings I have.