Are there spiders in Metamorphosis?

Yes, there are spiders in this game. I couldn't tell you how frequently they appear, but they definitely exist in this game. Based on images the spiders seem to be the hairless variety, similar to Skyrim's Frostbite spiders.

I suppose encountering arachnids to be expected based on a game where you regularly encounter other insects.

If you're feeling brave you can see it yourself from the image hosted front-and-center in this game review: https://www.pcinvasion.com/metamorphosis-review-between-angels-and-insects/