I went east to west, lived in Seattle for 21 years, and then moved back. Lifestyle and climate have definitely been the bigger factors in my clothing, since in both locations I've lived in/near large cities, take public transit to work, etc. For example, I do the same kind of work now, that I was doing when I left Seattle, and my colleagues dress with the same degree of formality. As for managing the transitions, I did let my high summer wardrobe grow smaller through attrition when I moved west, and am now building that back up. I'm in the mid-Atlantic area, so haven't felt the need to change my winter and transitional wardrobes. I did have a few heavy wool sweaters that were more indoor winter wear, 20+ years ago on the East coast, and then became transitional "outerwear" (when I didn't feel like wearing fleece) in Seattle. Interestingly, those are now languishing, but that could be because they're 20+ years old.
And, I totally agree with Vix's comment that "People are more chill..."- which makes it easy to wear what you want, and be more dressy if you feel like it. We have a dear friend who always wore heels to a huge party we threw every year in our back yard in Seattle, and she made it work. So, if you want to pull out your dressier items, just do it, and wear them with a smile!
I think you're on the right track to add the pieces that work for your lifestyle now, but take it slow. Give yourself another 6-12 months to see if your "East coast" clothes are part of this stage of life, and also try them in different combinations with some of your newer items. Enjoy the transition!