Brussels Airline

Yes, we flew Brussels Airlines from Brussels to Chicago in June. The plane and services were on par with United Airlines, no better, no worse. All went well.

Yes, Brussels Airlines is a member of the Star Alliance, which means you can book the trip on United, which is what I would do. It's a bit more energy getting a seat assignment and you need both a UA booking code as well as a Bru. booking code. BUT the advantage is if for some reason you have to cancel, the funds go back onto your UA account good for a year.

it's more than a member of Star Alliance - it's the Belgian subsidiary of Lufthansa

Yes, I flew them from Bordeaux to Brussels a couple years ago. It was a fine flight. One quirk, though. The plane had no corporate marketing on it anywhere. Nothing. Just a big, white airplane. Perhaps that is what they use for inter-europe flights...

IF the plane was white it was probably a temporary lease. Or it was between paint jobs.

Brussels Airlines often decorates its planes:
https://www.aviation24.be/airlines/lufthansa-group/brussels-airlines/belgian-icons-amare-aerosmurf-bruegel-magritte-rackham-trident/

the standard livery is mostly white with a few coloured dots at the rear, but livery has nothing to do with quality of service

https://www.brusselsairlines.com/bg/en/flying-with-us/our-fleet

Good airline, no difficulties with reservations or baggage. Planes were clean, food was good. Flew them four times a year over a two-year period when I worked in West Africa (I think their destinations have changed since then).