Does anyone know why Edge pops up this sign-in page when trying to enter a LF Forms Task?
That's almost certainly a system/policy setting rather than having anything to do with Forms directly.
This functionality relies on "integrated Windows authentication" and group policy typically controls what browsers/sites are able to access Windows credentials without additional prompts.
To narrow things down, I'd check the following:
It's hard to say exactly what the issue is because it really depends on your environment and what policies have been implemented, but the most common reason for this prompt is the integrated Windows authentication settings.
One thing I will note is that you seem to be accessing a public-facing URL and due to some of its vulnerabilities, integrated Windows Authentication is generally only recommended for intranet environments so that could also be a factor.
Do you get the popup when logging into the full Forms site or just when clicking the Task link?
I would start with adding your URL to the Local Intranet zone in Internet Options to see if that resolves it. If that works and your IT is comfortable with it, the change can be pushed down via GPO.