There are two different approaches, depending on whether you are working with the private repo strickly via Git itself or accessing it via npm.
As the logs show you using npm, I believe these are the correct instructions for you:
If you were getting the error as party of a submodule clone or a Git command run in the build command itself, then this would be the support guide to follow (but again, I do think the guide above is the right one for the issue in logs you posted):
If the solution in the top support guide above doesn’t work for you, please reply here to let us know what steps you tried and what the results were. Similarly, if there are questions about any of this, please let us know.