Object not rendered

what instructions? just remove all your custom script it will work with obj file, my site run this module every day

I don't have any custom scripts.

I mean remove

    <script type="importmap">
      {
        "imports": {
          "three": "https://unpkg.com/three@0.152.1/build/three.module.js",
          "three/addons/": "https://unpkg.com/three@0.152.1/examples/jsm/"
        }
      }
    </script>

look in https://git.drupalcode.org/project/threejs/-/blob/1.0.4/threejs.librarie...
you will see all loaded cdn.
try with field in Node not in paragraph

I removed the importmap script, and it's still not working. To address your initial question (what instructions?), the instructions i'm talking about are the ones in the description of the project:

Use CDN threejs
This module is based on https://github.com/eneus/drupal_threejs (but it's not totally the same I reuse about 30%).
How to use:

Enable modules Threejs + Threejs field
Configuration Threejs
Configuration field Threejs formatter

Support some format 3d like obj dae gltf stl....

some issue:
- camera fit to object (i set for scanner box)
- texture not work some case
- autorotation

I'm not familiar with the importmap script thing; how is the threejs library imported without that code?

I've tried downloading the file https://unpkg.com/three@0.152.1/build/three.module.js and including it using my theme library. When I do this, I can see that the threejs module is included in the HTML, but it still doesn't work.

Hum it's summary
the instructions start with "How to use" I never write, you must activate lib threejs cdn to work this module.
Install the new drupal 9 and active module, you can try with dev version. Do nothing you will see your object in 3D. if you have a bug report i will fix it if i have time

What is the recommended way to activate the threejs library with a CDN?

Nothing. you just need to install the module and enjoy it, it already includes the latest version threejs with cdn

Thanks; it's still not working in our production environment, but I was able to verify that it does work out of the box on a fresh install. So, presumably there's some template for preprocessing method that is breaking it. It appears to be a rendering issue; the field HTML isn't rendered at all.

@safetypin : Regarding your last comment, I also have the similar kind of issue in my website. Did you get any solution on it?

I disabled a bunch of modules and it started working, so I think it's an interaction with another module. I tried to go through and disable just a few modules at a time last week, but I haven't had time to finish figuring out which module it is.