Confusing Xbox game pass & PC Game pass?

I bought black ops 7 for my Xbox series s, played on it there, its great.

I want to play it on my laptop too with higher specs and higher hz refresh rate etc.

Since I bought the game for xbox series s and to play online I would need esstial membership?

And now if want to play it on pc or laptop I NEED a PC GAME PASS just to play it on there? Even if I have essential tier, and bought the game on xbox for xbox series s? So double charge membership monthly to play online on console and I had to buy the game, and then another money charge just to play it on pc monthly? Is this right?