The new Chromecast with Google TV, despite being stupidly named, ticks basically every single box here, except that it's $50, instead of $25-$35, but it's _fantastic_.

The remote is great, and includes a Google Assistant voice search button that's super useful, and the search is federated in the way you describe, and very good. It has support from every service, but it integrates really well with YouTubeTV, obviously, which is nice because there's a great Live tab with a guide. You can run the app store and install whatever Android TV app you want: I've installed NordVPN on mine to get around NHL.TV blackout bullshit.

AND it will get around a captive portal because it has a remote/browser, so you can use it in a hotel. Honestly, it's a delightful little device.