I had kinda the same dilemma, although I just wanted to change one of the bathrooms for the look of it, I’ll tell you, I could not find perfect matching brushed nickel for all the fixtures, like the shower system, faucet, etc., didn’t want to use all the same companies for everything but it’s almost impossible to match them so I threw in the towel. Chrome is pretty standard for every company. I have brushed nickel handles on every door in my house, best to keep it the same throughout the house for that, and they go fine with the chrome fixtures. So when in doubt, just use the same. I even decided to use the exact same cabinet pulls in all the bathrooms because I figured it was easier and more cohesive.

Ok to have different metals in different bathrooms. A nickel knob will seem ok with any.

For brushed nickel you will have to look at the manufacturers side by side. A true brushed nickel faucet should have a very slight gold undertone. Cabinet handles in brushed nickel are often more of a stainless look - again everything needs to be next to eachother to determine if they are close enough or a match. As for house doors you can do different colors on each side so if all the door knobs in the house are chrome you can have the chrome on the outside and do brushed nickel on the inside.

Don't over think it... just do your research..btw - I have different fixtures everywhere

Good luck

Door knobs are normally not considered a "fixture" in the bathroom. Fixtures include sink, pulls, towel bars, etc. Each bathroom is its own space with its own character. Perfectly fine to have them all be different from room to room! Chrome, nickel and brushed nickel are very similar and you can only tell them apart if they are side-by-side, so they are usually okay to include together in the same space following that trick! Good luck!