How do I use Web Components v3 in ASP.NET Core

[dongle-the-gadget]

Migrating my existing ASP.NET Core program from Web Components v2 (using <script type="module" src="https://unpkg.com/@@fluentui/web-components"></script>) to v3 (using <script type="module" src="https://unpkg.com/@@fluentui/web-components@beta"></script>) breaks the entire application: no styles or controls are being loaded.