Perhaps a truly minimalist shelter would be just sleeping in the dirt?
This kit is comprised of a cover tarp, a ground tarp, cordage, and stakes. It’s incredibly versatile (as long as you have a lot of cord!) anywhere with trees or other rigid objects to which you can tie your cord. Be sure to pull the cover tarp taught for best results (unlike the shitty job I did in the photo below).
The stakes and cord can tuck away in a bottle cage, while the tarps are so small and malleable they can go pretty much anywhere.