Perhaps a more diplomatic response for your question is that you are nowhere near the first, nor will you be the last, person to be confused on what benefits transfer when purchasing multi-carrier tickets.

Whether in the same alliance or not, there are often differences in policies. When it comes to things like lounge access these can vary a lot - and when those things matter a lot to you, it's always prudent to do some searching online to ensure what you wish to be true is actually true.

Airlines and travel booking websites often do not make it any easier (sometime more confusing).

For many of us, knowledge of these gotchas is common, and easy for us to know (also easy to be wrong). Definitely check around next time! Fortunately your main issue was just lounge access and shower quality. Others have gotten confused about luggage rights, access to preferred seating, even upgrades. Those can hurt a lot worse when wrong!

Safe travels!