Using org-level DOCUMENTER_KEY

In my lab's organization, we have several packages that lack their own documenter documentation, and so don't have a public/private key/secret pair for documenter. However, we do have an organization-level DOCUMENTER_KEY. One example of such a package is https://github.com/HolyLab/ExtractPSF.jl. I have CompatHelper set up but it fails. Here's the relevant section of the [log](https://github.com/HolyLab/ExtractPSF.jl/runs/5819047730?check_suite_focus=true):

```
Run import CompatHelper
import CompatHelper
CompatHelper.main()
shell: /usr/bin/julia --color=yes {0}
env:
GITHUB_TOKEN: ***
COMPATHELPER_PRIV: ***
Cloning into '/tmp/jl_Zl4CYh/REPO'...
Already on 'master'
Your branch is up to date with 'origin/master'.
Cloning into '/tmp/jl_b88E8j/General'...
[ Info: EnvVar `COMPATHELPER_PRIV` is defined, nonempty, and not `false`
[ Info: This doesn't look like a raw SSH private key. I will assume that it is a Base64-encoded SSH private key. I will now try to Base64-decode it.
[ Info: This was a Base64-encoded SSH private key. I Base64-decoded it, and now I have the raw SSH private key.
Cloning into 'REPO'...
Warning: Permanently added the RSA host key for IP address '140.82.112.4' to the list of known hosts.
git@github.com: Permission denied (publickey).
fatal: Could not read from remote repository.

Please make sure you have the correct access rights
and the repository exists.
```
and so on.

I'm wondering if there's an easy way around this, short of setting up keys for each individual repository? (There are ~20 such repos, so it would be nice to solve this at the organization level.)

Start with CompatHelper.main and the GitHub Actions environment shown in the issue log, especially DOCUMENTER_KEY and COMPATHELPER_PRIV handling. Trace how repository cloning authenticates with GitHub and determine what organization-level secret support would need to cover. Done means an organization-level key can support the described repositories without individual repository keys, with tests or documented verification for the workflow.

Written by the indexing model from the issue text.