Recording 360° video in unity is not a rectangle

Edit3:
Apparently this issue is caused by a Physical camerasetting on the camera component . Turning off Physical Camera will export equirectangular images/animations as expected.

The information below is still useful, but does not fully address this particular issue.

Your settings do not export an equirectangular image right now but a square image. Equirectangular images require to have an aspect ratio of 2:1. Whereas your current aspect ratio is 1:1.

In the Unity recorder settings you have set "360 view output" to 2048x2048. Resulting in the square image you're seeing. Try setting this to 4096x2048. This will produce a 4k image with an aspect ratio of 2:1, which should work for equirectangular projection.

See this page for more information about how equirectangular projection works. (emphasis mine)

Scanning cameras sometimes cover more than one 360° turn but software often assumes that equirectangular images cover 360° horizontally and 180° vertically, i.e. make sure that your equirectangular image has a proper aspect ratio of 2:1.

Edit:
Looking at the 2:1 picture it seems that Unity your records a cubemap, and not an equirectangular image. You may need to convert the cubemap to equirectangular using RenderTexture.ConvertToEquirect from the docs:

if (renderStereo)
{
    cubemap.ConvertToEquirect(equirect, Camera.MonoOrStereoscopicEye.Left);
    cubemap2.ConvertToEquirect(equirect, Camera.MonoOrStereoscopicEye.Right);
}

Take a look at this Unity bog which goes into further detail on how unity uses cubemaps/equirectangular projection From the blog:

After stereo cubemaps are generated, we can convert these cubemaps to stereo equirectangular maps which is a projection format used by 360 video players [...] To convert cubemaps to stereo equirectangular maps, call RenderTexture.ConvertToEquirect()

The "Cube map" width parameter on the Recorder may need to be tweaked for the desired result. But not sure which value would work best.

Edit2:
I created a test project (on GitHub ). However, despite (seemingly) the same setup, I don't get the same output as you. My output looks like a perfect equirectangular image (no need to do any transformations as I thought might be required as described in the first edit).

My setup:

output: