How does javascript version (asp-append-version) work in ASP.NET Core MVC?

You can check the LinkTagHelper source code, where you will see it is basically adding a version query string to the href value via a FileVersionProvider:

if (AppendVersion == true)
{
    EnsureFileVersionProvider();

    if (Href != null)
    {
        output.Attributes[HrefAttributeName].Value = _fileVersionProvider.AddFileVersionToPath(Href);
    }
}

private void EnsureFileVersionProvider()
{
    if (_fileVersionProvider == null)
    {
        _fileVersionProvider = new FileVersionProvider(
                HostingEnvironment.WebRootFileProvider,
                Cache,
                ViewContext.HttpContext.Request.PathBase);
    }
}

The FileVersionProvider will calculate the hash of the file contents using the SHA256 algorithm. It will then url encode it and add it to the query string as in:

path/to/file?v=B95ZXzHiOuQJzhBoHlSlNyN1_cOjJnz2DFsr-3ZyyJs

The hash will be recalculated only when the file changes, as it is added to the cache but with an expiration trigger based on a file watcher:

if (!_cache.TryGetValue(path, out value))
{
    value = QueryHelpers.AddQueryString(path, VersionKey, GetHashForFile(fileInfo));
    var cacheEntryOptions = new MemoryCacheEntryOptions().AddExpirationToken(_fileProvider.Watch(resolvedPath));
    _cache.Set(path, value, cacheEntryOptions);
}

This watcher is provided by HostingEnvironment.WebRootFileProvider, which implements IFileProvider:

//
// Summary:
//     Creates a change trigger with the specified filter.
//
// Parameters:
//   filter:
//     Filter string used to determine what files or folders to monitor. Example: **/*.cs,
//     *.*, subFolder/**/*.cshtml.
//
// Returns:
//     An Microsoft.Framework.Caching.IExpirationTrigger that is triggered when a file
//     matching filter is added, modified or deleted.
IExpirationTrigger Watch(string filter);

Note: You can see the cached values yourself by inspecting the values in the IMemoryCache:

//give the link:
<link rel="stylesheet" asp-append-version="true" href="~/css/site.css" />

//You can check the cached version
this.Context.RequestServices.GetRequiredService<IMemoryCache>().Get("/css/site.css")

//Which will show a value like:
/css/site.css?v=B95ZXzHiOuQJzhBoHlSlNyN1_cOjJnz2DFsr-3ZyyJs