Go mod tidy fails on private repository when git clone works

I put my ssh key in github so git clone works for a certain private repository; yet go mod tidy fails when trying to access the same repository, with the error message shown below. I could use help troubleshooting this problem. The error message from go mod tidy (redacting the name of the private repository, but otherwise verbatim) is:

    github.com/[private repository path]: cannot find module providing package github.com/[private repository path]: module github.com/[private repository path]: git ls-remote -q origin in /mnt/dependencies/gopath/pkg/mod/cache/vcs/a1f499df6a9855aecdc77bda31504008583a3268fdd403799aade71bb47df7d2: exit status 128:
fatal: 'origin' does not appear to be a git repository
fatal: Could not read from remote repository

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

The successful git clone command (again redacting the private repository) is:

git clone git@github.com:[private repository path].git

My .gitconfig file is (with my name and email redacted):

[user]
    name = [my name]
    email = [my email]

    insteadOf = https://github.com/
[core]
    excludesfile = /workdir/.gitignore

Other things that might make a difference:

• I am running commands as root in a Docker container.
• I tried to run go mod tidy on my host with the same key in ~/.ssh as I have on the Docker container, and I got login prompts, which github no longer supports (they want SSH keys or personal access tokens).
• The email in my gitconfig matches email given in the public key that I put on github.com.

A second, related question: Does the fact that I can run git clone rule out keys being uploaded wrong to github, and forgetting to enable SSO for the key on github?

Here is a similar question but it involves personal access tokens rather than ssh keys: https://stackoverflow.com/questions/71851732/go-mod-tidy-fails-to-download-private-github-repository

> I am running commands as root in a Docker container.

Make sure then it does access the same keys (in /root/.ssh) as the ones you are using with your regular account.

And check if the Git global config settings actually include your insteadOf directive.

> tried to run go mod tidy on my host with the same key in ~/.ssh as I have on the Docker container, and I got login prompts.

That means the public key is not properly registered to the GitHub user profile, or said user does not have the right to access the repository.

I found the answer to my problem, but it turns on a fact that I omitted in the question.

I didn't realize until the next morning that my Docker image had a higher version of golang than was used to populate $GOPATH (or at least I didn't realize how important this was). To fix this, I deleted everything under $GOPATH and re-ran go mod tidy with no issues.

The checklist in VonC's answer is useful and more to the point of the question as stated, so I accepted it. But I'll add to it for anyone that comes across this post:

"Is the version of golang used for go mod tidy different from what populated $GOPATH?"