Kalman filters are great! For people interested of one used in practice, it's used by Sendspin to keep speakers in sync, even works in browsers on phones on 5G etc.
Home Assistant [1] has been written using web components and it has been great. In 13 years that we've been around, we never had to do a full rewrite of the frontend but always have been able to gradually update components as needed. Not being tied to the JavaScript industry upgrade cycle (which is short!), has allowed us to pick our own priorities.
We currently use Lit for the framework on top (you do need one, that's fine). For state management we just pass props around, works great and allows community to easily develop custom cards that can plug into our frontend.
The downside is lack of available components. Although we're not tied to a single framework, and can pick any web component framework, the choices are somewhat limited. We're currently on material components and migrating some to Shoelace.
I talked more about our approach to frontend last year at the Syntax podcast[2].
This has never been the case. Custom elements are DOM Elements and so are just JavaScript objects. Just like you can do aEl.disabled = true, you can set any prop to any type of value.
Home Assistant is turning 8 years this week. To celebrate we have launched crowdfunding campaign for Home Assistant Amber, a device for both beginners and home automation enthusiasts and the easiest way to get started with Home Assistant.