This involves manually writing each sentence in key-value pairs and translating them, which will then be reflected in our system.

Yes. This is the default method to localize strings in applications. Some may use automatic translation for some parts of interface, but this can lead to inaccurate translations in some cases, depending on the quality of the translation to the requested language. Therefore, it's not a general method.

There are also platforms like Weblate where people can contribute to the localization of application strings.

For large applications like Facebook, Flipkart, and Amazon, is the process the same?

They usually do not disclose how they localize strings in their interfaces. As they have not introduced any other kind of tools or methods, we can infer that this is the case for them too.

To translate my application into multiple languages in a Blazor United Project and .NET 8, we need to use localization and resource files.

I recommend reading Blazor globalization and localization and Make an ASP.NET Core app's content localizable as they are the only resources you need to implement localization in Blazor.