[Feature]: Automatic HA Server Discovery

[Trooped]

Short Feature Title

Automatically Discover Your HA server via MDNS -> Zeroconf Sweep Fallback

What area does this affect?

User Interface (UI/UX), Home Assistant Integration (WebSocket)

The Problem

A lot of users seem to encounter problems with connecting to their HA instance manually (by providing the URL and port).
I suggest adding an automatic discovery feature of your HA instance, which will require some research and testing prior to implementing.

It's a feature I wanted to implement for a long time, but now I can do it with the help of the community!

The Proposed Solution

1. User wants to connect to his HA server (initial connection, or through settings screen's change URL)
2. The app will attempt to find the HA server in a background task, and display a list of matches to the user, from which he could choose the correct instance.
3. The app will then ask the user only for the LL-token.

Screenshots or Video

No response

Visuals / Mockups

No response

Additional Information

This solution will be based on this example repository I created.
What I need from the community:

1. Please let me know what you think of this feature in the comments of this discussion.
2. Please suggest how you think the UX for this should work (in terms of working alongside the current onboarding and connection implementation).
3. If you can - please run this python script on a local machine (after installing the zeroconf dependency), and let me know what's the result, and if there's something wrong/missing in the script (which we'll base the implementation on).
   DO NOT share your exact URL, but the port will be very helpful!

Home Assistant Context (Optional)

No response

Readiness Check

• I have confirmed this isn't already a feature/setting in the app by also searching the guide.
• I understand that this is an open-source project managed alongside a full-time job and B.Sc. studies by Omri, and PRs and Issues may take some time.
• I am willing to help provide more information upon request, and test beta builds of this feature.