what's wrong, tarragon?

My plant is sad.

I cleaned out all its dead stuff- lots- and gave it a new home. Succulent soil mix with a bit of richer potting soil and crushed eggshells stirred in. Inch layer of potting shards in the bottom for good drainage, and this pot sits inside another (the white decorative one doesn't have a drain hole).

At least what's left of the foliage looks healthy. I can't tell if the dried leaves/stems were from poor conditions- too much, too little water? or an insect pest. It seemed to have little spiderwebs stuck in the leaves but could be dust.

I broke off some tiny new shoots while stripping the dead leaves off, and tucked them into soil in case they can root and grow.

It's in a tall narrow pot because quite a bit had got leggy and hung down. Kind of pretty, but I don't know if that's normal, healthy growth habit for this plant, to have trailing stems.

I'm eating it again. Lovely in scrambled eggs.