Gray is on the way out. Listen to your designer. Everything sounds terrific!

White trim paint in a white that looks good with the wood tones, ie. cool or warm undertones.....wall paint a similar white for a fresh look, but I detest wood trim, but that is just an opinion....do one room aka the way the designer says, if you like it, do the rest of the house.

Pretty. Stain the trim like the floors. White trim might be okay as well, depending on the wall color. But gray won't work very well for the walls--I think you need something warmer. If tan is too brown (I understand that feeling), look into the whites. Be prepared to do a lot of test patches before finding the right one.

(I'd probably do the walls a light mossy green, but I usually always end up green somehow...)

I'd do the cabinet trim a black tone, it would accent the counter color and black goes well with the cabs.

I like the color she picked. Maybe it is just too dark for you. I don't think gray would be horrible if it was a grayish white.

To me the cabinets are bright enough. Not sure I would want another bright color.

No stained trim! You have a LOT of wood already and it is "strong" wood. I would use a light grayed/green for the walls and would do the woodwork in the same color. There is a lot going on in this kitchen! Your countertops and cabinets have a lot of movement. You need "calm" now. Look at Farrow & Ball's Lichen Green, but go a bit lighter.