I love hearing of your revelation, I had the same one years ago when I realized that it’s all one mountain range, just different sides of it. The Snoqualmie people, whose territory I live in, as with many of the ‘upriver’ tribes in Western Washington had close relationship with the tribes on the other side of pass, with intermarriage, exchange of goods and more. The Snoqualmie spoke the Yakama language (the tribe living on the eastern side of the mountain) as well as their own, and the local trade jargon, and many tribal members descent from Yakama lineage as well, and can remember their family members making the trek over 9,000 year old trails on horseback or by foot taking days to do so as they gathered and hunted along the way. There was definitely a cultural exchange as well, which showed up in the clothing, regalia and foods.
I spent a little time in Phoenix and Sedona, and I remember how exciting it was to discover this new set of plants, some familiar, some very different. To answer your question, one of the first things that came to my mind are the ponderosa pine, with needles which can be used to make the coil pine needle baskets, and the bear grass which tribes in Arizona used in the coil basketry technique to make amazing baskets and trays . I have one which is a treasured item. The coil basketry technique was really major with most of the tribes in Washington, primarily using cedar root, but adaptable to all these other plants. It is such a versatile and forgiving technique I love to teach it to beginners, especially those who think they won't be successful.
Other common plants between regions include chokecherry, which was crushed, seed and all, and dried to use as a form of pemmican, I imagine the use must have been similar there. I would imagine the medicinal uses would have been similar as well. Both regions have acorns which were undoubtedly used in Sedona, and both also had access to a form of pine nut (Pinyon pine in Sedona, Whitebark pine in the Cascades). I would imagine the techniques for processing these would have been similar. I saw many grinding stones up in the rocks outside of Phoenix.
Rabbitbrush, horsetail, scouring rush and cattail are common to both regions. Though different species there are also rose, alder, ash and willow. Their use for medicine, dye, and wood were almost certainly similar.
I've had the privilege of spending time with Warm Springs and Yakama Tribes of Eastern Washington and Oregon over the years , (this year I traveled on Canoe Journey for three weeks with the Warm Springs, Cowlitz and Chinook down the Columbia River through all of those bioregions), and I know that honoring the first harvest of foods, from roots to salmon to berries was an important practice. This practice of gratitude is something we can all keep alive. The use of sewn mats made from tule or cattail was also widespread, these were used to make mat houses which were useful winter and summer, and were lightweight and portable. I'm not sure of the tribal history in Sedona, it may have been more of a resource gathering area? When I think of Sedona I think of colorful red rock, I would be curious about the making and trade of pigment.
Of course you also have yucca and cactus and a bunch of other really cool plants less common here. Actually Prickly Pear is another commonalty between Eastern Washington and Arizona, not sure to what degree it was used here, but it was used for food and material. I made some pretty cool pigment crayons once by mixing prickly pear cactus gel from the leaf, with some powdered pigment, and maybe some oil (it's been a while). I used this directly on leather, which sort of worked with my beginner effort.
So I hope that kind of helps. When I went to Phoenix I went straight to the county history museums there (not the big famous art ones, though I did eventually), and visited a bunch of parks with interpretive trails, plant walks and etc, even the malls had landscapes with interpretive signage, and was amazed how fast it was to pick up on the plants there. I also went to Frank Lloyd Wright's place overlooking Phoenix, and thought that was a pretty amazing bit of design with lots of integration with the environment. There is a lot happening there with seed saving, traditional foods, and more. Great place.
Thanks for the thoughtful question, makes me want to get back down there and visit.