It's really hard to mix tans and grays successfully. They all need to be neutrals without undertones, and you need balance for a room that feels right.

You don't need to match your carpet to other rooms in the house if they don't connect. You don't need to use the same paint in the bath and the bedroom. You can have a tan/ivory/greige bedroom and a gray/white bath. A lot depends on how all the rooms connect to each other, and how much of them you see with all the doors open. Since you have a tan upholstered bed, I would use tan or beige carpet. Choose that first since you have less color options than paint. Use a lighter beige on the walls, like SW Shell White, which coordinates with SW Passive. Add white bedding and lots of textures. If you want some gray, add it through a few accessories so gray isn't the main color in the bedroom.

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no, you don't have to match the carpet. No you don't have to match the bathroom color unless they share the same walls.

what you're doing sounds very neutral. you can bring in navy or black for some contrast. try a coordinating color on the wall.

Here are some other tones that they have as coordinating w/Passive:

https://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW7064-passive#/7064/?s=coordinatingColors&p=PS0

Peppercorn and Grizzle gray are the darker charcoal colors. you could bring those in w/rugs, or pillows/throws or drapes/blinds. If you want a completely monotone room, then just stick w/what you have.

The bedroom can stand alone, so do what ever colors you like.

Thank you both so much. That was incredibly helpful and reassuring.