I had a similar issue. The fix for me was the remove the trailing slash ( / ) on your proxy_pass line.
I believe this is because the request URL that matches your location block includes the slash ( / ). So you are proxying https://minio/bucket//something which will fail on the ...
In this example configuration for a S3 Gateway, S3 API 403 errors get rewritten to 404 errors. You could possibly modify the configuration so that you could present NGINX 403 errors instead of 404 errors as the example uses.
NGINX S3 Gateway
My team at NGINX has published a fully functional (within Docker) example of how to proxy S3 API backends. It supports v2 and v4 authentication signatures. The meat of the implementation is done in njs and should be reasonably performant. Using that project as a reference, you may find a more comprehensive implementation that avoids some of ...
You can actually connect to S3 bucket from EC2 instance.
So you can build it. However, in case you have Veeam Enterprise and Enterprise Plus editions you can use SOBR to configure AWS S3 as a backup repository.