How can one set up a non-emitting environment map in cycles? If I set strength to 0, it is black. I tried doing something with Light Path node, but didn't succeed so far.
The above answer is way more complicated than it needs to be, just use compositing.
Just in render settings set Film to transparent and Color Management > View Transform to standard
Then in the compositing tab, use nodes and put an "Alpha Over" node between the two default nodes.
This video explains it perfectly: https://youtu.be/aegiN7XeLow?t=50