To be fair, when booking on AA.com, there is a link directly under the price with a link to “bag and optional fees”, which includes all of AA’s fees (bags, food/drink, WiFi) and a link for other operators including a link to BA’s page on seating.
I can understand why the OP didn’t click on it, but ultimately, it hasn’t been mis-sold by AA, just incorrect assumption made.
Ultimately, if you don’t have status then there is a need to factor in if you want specific seats and how much you’re prepared to pay in total. I very much still operate transactionally when booking flights and wouldn’t rule out organising a flight on a particular airline because I didn’t know how the operated, but OP is entitled to do so if they so wish.
We see similar complaints from BA flyers who fly with EI then find out they can’t guest or sometimes get access to the lounge.