BM Aura Bath & Spa is a bathroom paint that I used for my walls. It is a matte finish. I have Aura satin for the door and case work. But I may have purchased another line from BM for the cupboard I painted in satin. It really is a personal preference. I can't stand the tactile texture of a matte finish, so I don't rub my hands on my walls :) I love a smooth glossy finish to touch, so I like it at the doorway. But, I love the velvet LOOK of matte. For me it also depends on how many shiny surfaces I have. I like to play off of flat with a little shine and vise versa.

I'm not an expert but when choosing paint colors, I prefer contrast. I would get a few samples and paint some spots on the wall to see what works the best with your tile. If the tile leans more towards white I think a soft sage color would be pretty with the elements you've described, but if your tile leans towards a brown, it's hard to say. If you can post pictures, it would really help.

I like the creamy/off white tiles - way more than I like stark white. I think both your "Pixel White" & green paints tend toward cool, and they're both drawing attention to the warmer tile & highlighting the contrast. I'd re-paint the entire bathroom. If you can find a warm green, maybe a light olive and/or an off-white warm paint, the tiles will stand out less and look like they fit in. I have creamy tile in my kitchen, with two paint colors - an olive-y green and a rusty color. Here are a couple photos:

On colors, I think SW bagel might be a little rich and warm. I think a very low saturated sage or cream would work. Perhaps even a lighter version of the same hue you have now. Since you'll likely be taking things down to paint are you doing something with the medicine cabinet? Do you have enough storage w/o it? Would be good to see vanity as well. BTW, that tile doesn't bother me unless there is something we can't see in the photos.